%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA133-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:46 PM UTC 2026
% Result : Unsatisfiable 1.04s 1.23s
% Output : Proof 2.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA133-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 22:52:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 1.04/1.23 % SZS status Unsatisfiable
% 1.04/1.23 % SZS output start Proof
% 1.04/1.23 tff(r_type, type, (
% 1.04/1.23 r: ( $i * $i ) > $o)).
% 1.04/1.23 tff(s_type, type, (
% 1.04/1.23 s: $i > $i)).
% 1.04/1.23 tff(z_type, type, (
% 1.04/1.23 z: $i)).
% 1.04/1.23 tff(elem_1_type, type, (
% 1.04/1.23 elem_1: $i)).
% 1.04/1.23 tff(b_type, type, (
% 1.04/1.23 b: ( $i * $i ) > $o)).
% 1.04/1.23 tff(inj_0_type, type, (
% 1.04/1.23 inj_0: $i > $i)).
% 1.04/1.23 tff(1,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.04/1.23 tff(2,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.04/1.23 tff(3,plain,
% 1.04/1.23 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.04/1.23 inference(bind,[status(th)],[])).
% 1.04/1.23 tff(4,plain,
% 1.04/1.23 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.04/1.23 inference(quant_intro,[status(thm)],[3])).
% 1.04/1.23 tff(5,plain,
% 1.04/1.23 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(6,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.04/1.23 tff(7,plain,
% 1.04/1.23 (![X: $i] : (~(s(X) = z))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.04/1.23 tff(8,plain,(
% 1.04/1.23 ![X: $i] : (~(s(X) = z))),
% 1.04/1.23 inference(skolemize,[status(sab)],[7])).
% 1.04/1.23 tff(9,plain,
% 1.04/1.23 (![X: $i] : (~(s(X) = z))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.04/1.23 tff(10,plain,
% 1.04/1.23 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(11,plain,
% 1.04/1.23 (~(s(s(z)) = z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[10, 9])).
% 1.04/1.23 tff(12,plain,
% 1.04/1.23 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.04/1.23 inference(bind,[status(th)],[])).
% 1.04/1.23 tff(13,plain,
% 1.04/1.23 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.04/1.23 inference(quant_intro,[status(thm)],[12])).
% 1.04/1.23 tff(14,plain,
% 1.04/1.23 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(15,plain,
% 1.04/1.23 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.04/1.23 inference(bind,[status(th)],[])).
% 1.04/1.23 tff(16,plain,
% 1.04/1.23 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.04/1.24 inference(quant_intro,[status(thm)],[15])).
% 1.04/1.24 tff(17,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.04/1.24 tff(18,plain,
% 1.04/1.24 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.04/1.24 tff(19,plain,
% 1.04/1.24 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.04/1.24 tff(20,plain,(
% 1.04/1.24 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.04/1.24 inference(skolemize,[status(sab)],[19])).
% 1.04/1.24 tff(21,plain,
% 1.04/1.24 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.04/1.24 tff(22,plain,
% 1.04/1.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(23,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(24,plain,
% 1.04/1.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.04/1.24 tff(25,plain,
% 1.04/1.24 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 1.04/1.24 tff(26,plain,
% 1.04/1.24 (r(s(s(z)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[25, 2])).
% 1.04/1.24 tff(27,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.04/1.24 tff(28,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.04/1.24 tff(29,plain,
% 1.04/1.24 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(30,plain,
% 1.04/1.24 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(31,plain,
% 1.04/1.24 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(32,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.04/1.24 tff(33,plain,
% 1.04/1.24 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.04/1.24 tff(34,plain,(
% 1.04/1.24 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.04/1.24 inference(skolemize,[status(sab)],[33])).
% 1.04/1.24 tff(35,plain,
% 1.04/1.24 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.04/1.24 tff(36,plain,
% 1.04/1.24 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[35, 29])).
% 1.04/1.24 tff(37,plain,
% 1.04/1.24 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(38,plain,
% 1.04/1.24 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[37, 36])).
% 1.04/1.24 tff(39,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.04/1.24 tff(40,plain,
% 1.04/1.24 (s(s(z)) = s(s(s(z)))),
% 1.04/1.24 inference(symmetry,[status(thm)],[39])).
% 1.04/1.24 tff(41,plain,
% 1.04/1.24 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[40])).
% 1.04/1.24 tff(42,plain,
% 1.04/1.24 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(43,plain,
% 1.04/1.24 (inj_0(s(s(z))) = s(z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[42, 36])).
% 1.04/1.24 tff(44,plain,
% 1.04/1.24 (s(z) = inj_0(s(s(z)))),
% 1.04/1.24 inference(symmetry,[status(thm)],[43])).
% 1.04/1.24 tff(45,plain,
% 1.04/1.24 (s(z) = s(s(z))),
% 1.04/1.24 inference(transitivity,[status(thm)],[44, 41, 38])).
% 1.04/1.24 tff(46,plain,
% 1.04/1.24 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(47,plain,
% 1.04/1.24 (inj_0(s(z)) = z),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[46, 36])).
% 1.04/1.24 tff(48,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.04/1.24 tff(49,plain,
% 1.04/1.24 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[48])).
% 1.04/1.24 tff(50,plain,
% 1.04/1.24 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.04/1.24 inference(symmetry,[status(thm)],[49])).
% 1.04/1.24 tff(51,plain,
% 1.04/1.24 (s(s(z)) = s(z)),
% 1.04/1.24 inference(symmetry,[status(thm)],[48])).
% 1.04/1.24 tff(52,plain,
% 1.04/1.24 (s(s(z)) = z),
% 1.04/1.24 inference(transitivity,[status(thm)],[51, 44, 50, 47])).
% 1.04/1.24 tff(53,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[11, 52])).
% 1.04/1.24 tff(54,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(55,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[54, 45])).
% 1.04/1.24 tff(56,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(57,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.04/1.24 tff(58,plain,
% 1.04/1.24 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(59,plain,
% 1.04/1.24 (~(s(s(s(z))) = z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[58, 9])).
% 1.04/1.24 tff(60,plain,
% 1.04/1.24 (((~![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))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(61,plain,
% 1.04/1.24 ((~![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))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(62,plain,
% 1.04/1.24 ((~![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)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.04/1.24 tff(63,plain,
% 1.04/1.24 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[62, 21, 59])).
% 1.04/1.24 tff(64,plain,
% 1.04/1.24 (r(s(s(s(z))), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[63, 57])).
% 1.04/1.24 tff(65,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.04/1.24 tff(66,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.04/1.24 tff(67,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.04/1.24 tff(68,plain,
% 1.04/1.24 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))),
% 1.04/1.24 inference(bind,[status(th)],[])).
% 1.04/1.24 tff(69,plain,
% 1.04/1.24 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.04/1.24 inference(quant_intro,[status(thm)],[68])).
% 1.04/1.24 tff(70,plain,
% 1.04/1.24 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(71,plain,
% 1.04/1.24 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r(X0, X1)) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> (((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> (((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))))), rewrite((((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))))),
% 1.04/1.24 inference(bind,[status(th)],[])).
% 1.04/1.24 tff(72,plain,
% 1.04/1.24 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.04/1.24 inference(quant_intro,[status(thm)],[71])).
% 1.04/1.24 tff(73,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.04/1.24 tff(74,plain,
% 1.04/1.24 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.04/1.24 tff(75,plain,
% 1.04/1.24 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.04/1.24 tff(76,plain,(
% 1.04/1.24 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.04/1.24 inference(skolemize,[status(sab)],[75])).
% 1.04/1.24 tff(77,plain,
% 1.04/1.24 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.04/1.24 tff(78,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(79,plain,
% 1.04/1.24 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(80,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[79])).
% 1.04/1.24 tff(81,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.04/1.24 inference(transitivity,[status(thm)],[80, 78])).
% 1.04/1.24 tff(82,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(83,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.04/1.24 tff(84,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[83, 77, 67, 66, 65])).
% 1.04/1.24 tff(85,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(86,plain,
% 1.04/1.24 (~r(s(s(s(z))), s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[85, 64, 26])).
% 1.04/1.24 tff(87,plain,
% 1.04/1.24 (((~![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))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(88,plain,
% 1.04/1.24 ((~![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))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(89,plain,
% 1.04/1.24 ((~![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)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.04/1.24 tff(90,plain,
% 1.04/1.24 (b(s(s(s(z))), s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[89, 21, 86, 56])).
% 1.04/1.24 tff(91,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(92,plain,
% 1.04/1.24 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(93,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[92])).
% 1.04/1.24 tff(94,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.04/1.24 inference(transitivity,[status(thm)],[93, 91])).
% 1.04/1.24 tff(95,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(96,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.04/1.24 tff(97,plain,
% 1.04/1.24 (~r(s(s(z)), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[96, 77, 64, 26])).
% 1.04/1.24 tff(98,plain,
% 1.04/1.24 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.04/1.24 inference(commutativity,[status(thm)],[])).
% 1.04/1.24 tff(99,plain,
% 1.04/1.24 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[98])).
% 1.04/1.24 tff(100,plain,
% 1.04/1.24 (~(s(s(z)) = s(s(s(z))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[56, 99])).
% 1.04/1.24 tff(101,plain,
% 1.04/1.24 (((~![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)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(102,plain,
% 1.04/1.24 ((~![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)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(103,plain,
% 1.04/1.24 ((~![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))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.04/1.24 tff(104,plain,
% 1.04/1.24 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[103, 21])).
% 1.04/1.24 tff(105,plain,
% 1.04/1.24 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[104, 100])).
% 1.04/1.24 tff(106,plain,
% 1.04/1.24 (b(s(s(z)), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[105, 97])).
% 1.04/1.24 tff(107,plain,
% 1.04/1.24 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.04/1.24 inference(bind,[status(th)],[])).
% 1.04/1.24 tff(108,plain,
% 1.04/1.24 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.04/1.24 inference(quant_intro,[status(thm)],[107])).
% 1.04/1.24 tff(109,plain,
% 1.04/1.24 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(110,plain,
% 1.04/1.24 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.04/1.24 inference(bind,[status(th)],[])).
% 1.04/1.24 tff(111,plain,
% 1.04/1.24 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.04/1.24 inference(quant_intro,[status(thm)],[110])).
% 1.04/1.24 tff(112,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.04/1.24 tff(113,plain,
% 1.04/1.24 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.04/1.24 tff(114,plain,
% 1.04/1.24 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[113, 109])).
% 1.04/1.24 tff(115,plain,(
% 1.04/1.24 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.04/1.24 inference(skolemize,[status(sab)],[114])).
% 1.04/1.24 tff(116,plain,
% 1.04/1.24 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[115, 108])).
% 1.04/1.24 tff(117,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(118,plain,
% 1.04/1.24 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(119,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[118])).
% 1.04/1.24 tff(120,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[119, 117])).
% 1.04/1.24 tff(121,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(122,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.04/1.24 tff(123,plain,
% 1.04/1.24 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[122, 116, 106, 28, 90])).
% 1.04/1.24 tff(124,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.04/1.24 tff(125,plain,
% 1.04/1.24 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[124])).
% 1.04/1.24 tff(126,plain,
% 1.04/1.24 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(127,plain,
% 1.04/1.24 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[126, 36])).
% 1.04/1.24 tff(128,plain,
% 1.04/1.24 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.04/1.24 inference(symmetry,[status(thm)],[127])).
% 1.04/1.24 tff(129,plain,
% 1.04/1.24 (s(s(s(z))) = s(z)),
% 1.04/1.24 inference(transitivity,[status(thm)],[128, 125, 43])).
% 1.04/1.24 tff(130,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.04/1.24 tff(131,plain,
% 1.04/1.24 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[130])).
% 1.04/1.24 tff(132,plain,
% 1.04/1.24 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.04/1.24 inference(symmetry,[status(thm)],[38])).
% 1.04/1.24 tff(133,plain,
% 1.04/1.24 (s(s(z)) = z),
% 1.04/1.24 inference(transitivity,[status(thm)],[132, 131, 47])).
% 1.04/1.24 tff(134,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[11, 133])).
% 1.04/1.24 tff(135,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(136,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[135, 129])).
% 1.04/1.24 tff(137,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(138,plain,
% 1.04/1.24 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.04/1.24 inference(commutativity,[status(thm)],[])).
% 1.04/1.24 tff(139,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.24 tff(140,plain,
% 1.04/1.24 (s(s(s(s(z)))) = s(s(z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.04/1.24 tff(141,assumption,(~(s(s(s(s(z)))) = s(s(z)))), introduced(assumption)).
% 1.04/1.24 tff(142,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[141, 140])).
% 1.04/1.24 tff(143,plain,((~(s(s(z)) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(144,plain,
% 1.04/1.24 (~(s(s(z)) = s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[143, 137])).
% 1.04/1.24 tff(145,plain,
% 1.04/1.24 (((~![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))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(146,plain,
% 1.04/1.24 ((~![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))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(147,plain,
% 1.04/1.24 ((~![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)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.04/1.24 tff(148,plain,
% 1.04/1.24 ((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)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[147, 21])).
% 1.04/1.24 tff(149,plain,
% 1.04/1.24 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[148, 144])).
% 1.04/1.24 tff(150,plain,
% 1.04/1.24 (r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[149, 123])).
% 1.04/1.24 tff(151,plain,
% 1.04/1.24 (~r(s(s(z)), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[96, 77, 67, 66])).
% 1.04/1.24 tff(152,plain,
% 1.04/1.24 (b(s(s(z)), s(s(s(z))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[105, 151])).
% 1.04/1.24 tff(153,plain,
% 1.04/1.24 (~r(s(s(s(z))), s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[85, 67, 66])).
% 1.04/1.24 tff(154,plain,
% 1.04/1.24 (b(s(s(s(z))), s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[89, 21, 153, 56])).
% 1.04/1.24 tff(155,assumption,(r(s(z), z)), introduced(assumption)).
% 1.04/1.24 tff(156,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.04/1.24 tff(157,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(158,plain,
% 1.04/1.24 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(159,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[158])).
% 1.04/1.24 tff(160,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[159, 157])).
% 1.04/1.25 tff(161,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(162,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.04/1.25 tff(163,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[162, 77, 155, 66, 156])).
% 1.04/1.25 tff(164,plain,((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(165,plain,
% 1.04/1.25 (~r(s(z), s(s(z)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[164, 155, 66])).
% 1.04/1.25 tff(166,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.04/1.25 tff(167,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 1.04/1.25 tff(168,plain,
% 1.04/1.25 (((~![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))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(169,plain,
% 1.04/1.25 ((~![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))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(170,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.04/1.25 tff(171,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[170, 21, 54, 167, 166])).
% 1.04/1.25 tff(172,plain,(r(s(z), s(s(z))) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(173,plain,
% 1.04/1.25 (b(s(z), s(s(z)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[172, 165])).
% 1.04/1.25 tff(174,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.04/1.25 tff(175,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.04/1.25 tff(176,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.04/1.25 tff(177,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(178,plain,
% 1.04/1.25 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(179,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[178])).
% 1.04/1.25 tff(180,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[179, 177])).
% 1.04/1.25 tff(181,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(182,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.04/1.25 tff(183,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[182, 116, 27, 176, 175, 174])).
% 1.04/1.25 tff(184,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(185,plain,
% 1.04/1.25 (~b(s(z), s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[184, 173, 154, 152])).
% 1.04/1.25 tff(186,plain,
% 1.04/1.25 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.04/1.25 inference(commutativity,[status(thm)],[])).
% 1.04/1.25 tff(187,plain,
% 1.04/1.25 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.04/1.25 inference(symmetry,[status(thm)],[186])).
% 1.04/1.25 tff(188,plain,
% 1.04/1.25 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[187])).
% 1.04/1.25 tff(189,plain,
% 1.04/1.25 (~(s(z) = s(s(s(z))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[135, 188])).
% 1.04/1.25 tff(190,plain,
% 1.04/1.25 (((~![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)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(191,plain,
% 1.04/1.25 ((~![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)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(192,plain,
% 1.04/1.25 ((~![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))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.04/1.25 tff(193,plain,
% 1.04/1.25 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[192, 21])).
% 1.04/1.25 tff(194,plain,
% 1.04/1.25 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[193, 189])).
% 1.04/1.25 tff(195,plain,
% 1.04/1.25 (r(s(z), s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[194, 185])).
% 1.04/1.25 tff(196,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(197,plain,
% 1.04/1.25 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(198,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[197])).
% 1.04/1.25 tff(199,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 1.04/1.25 inference(transitivity,[status(thm)],[198, 196])).
% 1.04/1.25 tff(200,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(201,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.04/1.25 tff(202,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[201, 77, 155, 67, 195])).
% 1.04/1.25 tff(203,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(204,plain,
% 1.04/1.25 (~r(s(z), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[203, 64, 26])).
% 1.04/1.25 tff(205,plain,
% 1.04/1.25 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(206,plain,
% 1.04/1.25 (~(s(z) = z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[205, 9])).
% 1.04/1.25 tff(207,plain,
% 1.04/1.25 (((~![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))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(208,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(209,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.04/1.25 tff(210,plain,
% 1.04/1.25 (b(s(z), z) | r(s(z), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[209, 21, 206])).
% 1.04/1.25 tff(211,plain,
% 1.04/1.25 (b(s(z), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[210, 204])).
% 1.04/1.25 tff(212,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.04/1.25 tff(213,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(214,plain,
% 1.04/1.25 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(215,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[214])).
% 1.04/1.25 tff(216,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[215, 213])).
% 1.04/1.25 tff(217,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(218,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.04/1.25 tff(219,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[218, 116, 212, 27, 28, 176])).
% 1.04/1.25 tff(220,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(221,plain,
% 1.04/1.25 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[220, 90, 28, 106])).
% 1.04/1.25 tff(222,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![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))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(223,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(224,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.04/1.25 tff(225,plain,
% 1.04/1.25 ((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)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[224, 21])).
% 1.04/1.25 tff(226,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[225, 137])).
% 1.04/1.25 tff(227,plain,
% 1.04/1.25 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[226, 221])).
% 1.04/1.25 tff(228,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.04/1.25 tff(229,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.04/1.25 tff(230,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(231,plain,
% 1.04/1.25 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(232,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[231])).
% 1.04/1.25 tff(233,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.04/1.25 inference(transitivity,[status(thm)],[232, 230])).
% 1.04/1.25 tff(234,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(235,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.04/1.25 tff(236,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[235, 77, 229, 66, 228])).
% 1.04/1.25 tff(237,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(238,plain,
% 1.04/1.25 (~r(s(s(s(s(z)))), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[237, 227, 26])).
% 1.04/1.25 tff(239,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.04/1.25 tff(240,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.04/1.25 tff(241,plain,
% 1.04/1.25 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(242,plain,
% 1.04/1.25 (~(s(s(s(s(z)))) = z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[241, 9])).
% 1.04/1.25 tff(243,plain,
% 1.04/1.25 (((~![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))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(244,plain,
% 1.04/1.25 ((~![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))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(245,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.04/1.25 tff(246,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[245, 21, 242, 240, 239])).
% 1.04/1.25 tff(247,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(248,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[247, 238])).
% 1.04/1.25 tff(249,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.25 tff(250,plain,
% 1.04/1.25 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.04/1.25 inference(commutativity,[status(thm)],[])).
% 1.04/1.25 tff(251,plain,
% 1.04/1.25 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.04/1.25 inference(symmetry,[status(thm)],[250])).
% 1.04/1.25 tff(252,plain,
% 1.04/1.25 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[251])).
% 1.04/1.25 tff(253,plain,
% 1.04/1.25 (~(z = s(s(s(z))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[59, 252])).
% 1.04/1.25 tff(254,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.04/1.25 tff(255,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.04/1.25 tff(256,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(257,plain,
% 1.04/1.25 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(258,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[257])).
% 1.04/1.25 tff(259,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[258, 256])).
% 1.04/1.25 tff(260,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(261,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.04/1.25 tff(262,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[261, 116, 255, 27, 28, 254, 176])).
% 1.04/1.25 tff(263,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(264,plain,
% 1.04/1.25 (~b(z, s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[263, 27, 28, 254, 176])).
% 1.04/1.25 tff(265,plain,
% 1.04/1.25 (((~![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)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(266,plain,
% 1.04/1.25 ((~![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)))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(267,plain,
% 1.04/1.25 ((~![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))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.04/1.25 tff(268,plain,
% 1.04/1.25 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[267, 21, 264])).
% 1.04/1.25 tff(269,plain,
% 1.04/1.25 (r(z, s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[268, 253])).
% 1.04/1.25 tff(270,assumption,(b(s(z), z)), introduced(assumption)).
% 1.04/1.25 tff(271,assumption,(b(z, s(z))), introduced(assumption)).
% 1.04/1.25 tff(272,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(273,plain,
% 1.04/1.25 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(274,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[273])).
% 1.04/1.25 tff(275,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[274, 272])).
% 1.04/1.26 tff(276,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(277,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.04/1.26 tff(278,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[277, 116, 270, 271, 254, 249])).
% 1.04/1.26 tff(279,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(280,plain,
% 1.04/1.26 (~b(z, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[279, 249, 254, 270])).
% 1.04/1.26 tff(281,plain,
% 1.04/1.26 ((z = s(z)) <=> (s(z) = z)),
% 1.04/1.26 inference(commutativity,[status(thm)],[])).
% 1.04/1.26 tff(282,plain,
% 1.04/1.26 ((s(z) = z) <=> (z = s(z))),
% 1.04/1.26 inference(symmetry,[status(thm)],[281])).
% 1.04/1.26 tff(283,plain,
% 1.04/1.26 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[282])).
% 1.04/1.26 tff(284,plain,
% 1.04/1.26 (~(z = s(z))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[206, 283])).
% 1.04/1.26 tff(285,plain,
% 1.04/1.26 (((~![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)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(286,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(287,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.04/1.26 tff(288,plain,
% 1.04/1.26 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[287, 21])).
% 1.04/1.26 tff(289,plain,
% 1.04/1.26 (b(z, s(z)) | r(z, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[288, 284])).
% 1.04/1.26 tff(290,plain,
% 1.04/1.26 (r(z, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[289, 280])).
% 1.04/1.26 tff(291,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(292,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(293,assumption,(r(z, s(z))), introduced(assumption)).
% 1.04/1.26 tff(294,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(295,plain,
% 1.04/1.26 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(296,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[295])).
% 1.04/1.26 tff(297,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[296, 294])).
% 1.04/1.26 tff(298,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(299,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.04/1.26 tff(300,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[299, 77, 293, 292, 291])).
% 1.04/1.26 tff(301,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(302,plain,
% 1.04/1.26 (~r(s(z), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[301, 290, 269])).
% 1.04/1.26 tff(303,plain,
% 1.04/1.26 (b(s(z), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[194, 302])).
% 1.04/1.26 tff(304,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(305,plain,
% 1.04/1.26 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(306,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[305])).
% 1.04/1.26 tff(307,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[306, 304])).
% 1.04/1.26 tff(308,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(309,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[308, 307])).
% 1.04/1.26 tff(310,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[309, 116, 27, 28, 176, 303, 249])).
% 1.04/1.26 tff(311,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(312,plain,
% 1.04/1.26 (~b(s(z), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[311, 106, 28, 90, 248, 211])).
% 1.04/1.26 tff(313,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(314,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(315,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(316,plain,
% 1.04/1.26 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[315])).
% 1.04/1.26 tff(317,plain,
% 1.04/1.26 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.04/1.26 inference(symmetry,[status(thm)],[316])).
% 1.04/1.26 tff(318,plain,
% 1.04/1.26 (s(s(s(z))) = z),
% 1.04/1.26 inference(transitivity,[status(thm)],[128, 317, 47])).
% 1.04/1.26 tff(319,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[59, 318])).
% 1.04/1.26 tff(320,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(321,plain,
% 1.04/1.26 (((~![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))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(322,plain,
% 1.04/1.26 ((~![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))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(323,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.04/1.26 tff(324,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[323, 21, 320, 314, 313])).
% 1.04/1.26 tff(325,plain,(b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(326,plain,
% 1.04/1.26 (r(s(z), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[325, 312])).
% 1.04/1.26 tff(327,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(328,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(329,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(330,plain,
% 1.04/1.26 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(331,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[330])).
% 1.04/1.26 tff(332,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[331, 329])).
% 1.04/1.26 tff(333,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(334,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.04/1.26 tff(335,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[334, 77, 328, 156, 327])).
% 1.04/1.26 tff(336,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(337,plain,
% 1.04/1.26 (~r(s(z), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[336, 326, 150])).
% 1.04/1.26 tff(338,plain,
% 1.04/1.26 (b(s(z), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[172, 337])).
% 1.04/1.26 tff(339,plain,
% 1.04/1.26 (~b(s(z), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[184, 338, 90, 106])).
% 1.04/1.26 tff(340,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.04/1.26 tff(341,plain,
% 1.04/1.26 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[122, 116, 27, 28, 176])).
% 1.04/1.26 tff(342,plain,
% 1.04/1.26 (r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[149, 341])).
% 1.04/1.26 tff(343,plain,
% 1.04/1.26 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[220, 176, 28, 27])).
% 1.04/1.26 tff(344,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[226, 343])).
% 1.04/1.26 tff(345,plain,
% 1.04/1.26 (~r(s(s(s(s(z)))), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[237, 344, 26])).
% 1.04/1.26 tff(346,plain,
% 1.04/1.26 (b(s(s(s(s(z)))), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[247, 345])).
% 1.04/1.26 tff(347,plain,
% 1.04/1.26 (~b(s(z), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[311, 27, 28, 176, 346, 270])).
% 1.04/1.26 tff(348,plain,
% 1.04/1.26 (r(s(z), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[325, 347])).
% 1.04/1.26 tff(349,plain,
% 1.04/1.26 (~r(s(z), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[336, 348, 342])).
% 1.04/1.26 tff(350,plain,
% 1.04/1.26 (b(s(z), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[172, 349])).
% 1.04/1.26 tff(351,plain,
% 1.04/1.26 (~b(s(z), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[184, 350, 176, 27])).
% 1.04/1.26 tff(352,plain,
% 1.04/1.26 (r(s(z), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[194, 351])).
% 1.04/1.26 tff(353,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.04/1.26 tff(354,plain,
% 1.04/1.26 (((~![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))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(355,plain,
% 1.04/1.26 ((~![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))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(356,plain,
% 1.04/1.26 ((~![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)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.04/1.26 tff(357,plain,
% 1.04/1.26 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[356, 21])).
% 1.04/1.26 tff(358,plain,
% 1.04/1.26 (r(s(z), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[357, 353, 340])).
% 1.04/1.26 tff(359,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(360,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.04/1.26 tff(361,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(362,plain,
% 1.04/1.26 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(363,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[362])).
% 1.04/1.26 tff(364,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[363, 361])).
% 1.04/1.26 tff(365,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(366,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[365, 364])).
% 1.04/1.26 tff(367,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[366, 77, 360, 359, 292])).
% 1.04/1.26 tff(368,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(369,plain,
% 1.04/1.26 (~r(elem!1, s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[368, 358, 352])).
% 1.04/1.26 tff(370,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.04/1.26 tff(371,plain,
% 1.04/1.26 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 1.04/1.26 inference(monotonicity,[status(thm)],[370])).
% 1.04/1.26 tff(372,plain,
% 1.04/1.26 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.04/1.26 inference(symmetry,[status(thm)],[371])).
% 1.04/1.26 tff(373,plain,
% 1.04/1.26 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(z))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[372])).
% 1.04/1.26 tff(374,plain,
% 1.04/1.26 (~b(s(z), s(s(z)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[340, 373])).
% 1.04/1.26 tff(375,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[174, 374])).
% 1.04/1.26 tff(376,plain,((~(s(s(z)) = elem!1)) | (~b(s(z), s(s(z)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(377,plain,
% 1.04/1.26 (~(s(s(z)) = elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[376, 340, 350])).
% 1.04/1.26 tff(378,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(379,plain,
% 1.04/1.26 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(380,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[379])).
% 1.04/1.26 tff(381,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[380, 378])).
% 1.04/1.26 tff(382,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(383,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[382, 381])).
% 1.04/1.26 tff(384,plain,
% 1.04/1.26 (~r(s(s(z)), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[383, 77, 342, 348])).
% 1.04/1.26 tff(385,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.04/1.26 tff(386,plain,
% 1.04/1.26 (s(z) = s(s(z))),
% 1.04/1.26 inference(symmetry,[status(thm)],[385])).
% 1.04/1.26 tff(387,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[54, 386])).
% 1.04/1.26 tff(388,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(389,plain,
% 1.04/1.26 (((~![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)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(390,plain,
% 1.04/1.26 ((~![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)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(391,plain,
% 1.04/1.26 ((~![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))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.04/1.26 tff(392,plain,
% 1.04/1.26 (b(s(s(z)), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[391, 21, 388, 384])).
% 1.04/1.26 tff(393,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(394,plain,
% 1.04/1.26 (((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(395,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[394])).
% 1.04/1.26 tff(396,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[395, 393])).
% 1.04/1.26 tff(397,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(398,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[397, 396])).
% 1.04/1.26 tff(399,plain,
% 1.04/1.26 (~b(s(s(s(z))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[398, 116, 270, 176, 392, 350])).
% 1.04/1.26 tff(400,plain,
% 1.04/1.26 (((~![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)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(401,plain,
% 1.04/1.26 ((~![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)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(402,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.04/1.26 tff(403,plain,
% 1.04/1.26 (r(s(s(s(z))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[402, 21, 135, 399])).
% 1.04/1.26 tff(404,assumption,(elem!1 = z), introduced(assumption)).
% 1.04/1.26 tff(405,plain,
% 1.04/1.26 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.04/1.26 inference(monotonicity,[status(thm)],[404])).
% 1.04/1.26 tff(406,plain,
% 1.04/1.26 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.04/1.26 inference(symmetry,[status(thm)],[405])).
% 1.04/1.26 tff(407,plain,
% 1.04/1.26 (b(s(z), elem!1)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[270, 406])).
% 1.04/1.26 tff(408,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[340, 407])).
% 1.04/1.26 tff(409,plain,((~(elem!1 = z)) | b(s(z), elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(410,plain,
% 1.04/1.26 (~(elem!1 = z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[409, 340, 270])).
% 1.04/1.26 tff(411,plain,
% 1.04/1.26 (~b(z, s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[263, 27, 28, 346, 176])).
% 1.04/1.26 tff(412,plain,
% 1.04/1.26 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[267, 21, 411])).
% 1.04/1.26 tff(413,plain,
% 1.04/1.26 (r(z, s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[412, 253])).
% 1.04/1.26 tff(414,plain,
% 1.04/1.26 (~r(z, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[301, 352, 413])).
% 1.04/1.26 tff(415,plain,
% 1.04/1.26 (b(z, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[289, 414])).
% 1.04/1.26 tff(416,plain,
% 1.04/1.26 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.04/1.26 inference(commutativity,[status(thm)],[])).
% 1.04/1.26 tff(417,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.04/1.26 tff(418,plain,
% 1.04/1.26 (s(z) = elem!1),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.04/1.26 tff(419,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[353, 418])).
% 1.04/1.26 tff(420,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(421,plain,
% 1.04/1.26 (~(elem!1 = s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[420, 353])).
% 1.04/1.26 tff(422,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.04/1.26 tff(423,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(424,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(425,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.04/1.26 tff(426,plain,
% 1.04/1.26 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[425, 21])).
% 1.04/1.26 tff(427,plain,
% 1.04/1.26 (r(s(s(z)), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[426, 1, 422])).
% 1.04/1.26 tff(428,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.04/1.26 tff(429,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(430,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(431,plain,
% 1.04/1.27 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(432,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[431])).
% 1.04/1.27 tff(433,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[432, 430])).
% 1.04/1.27 tff(434,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(435,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.04/1.27 tff(436,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[435, 77, 429, 428, 328])).
% 1.04/1.27 tff(437,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(438,plain,
% 1.04/1.27 (~r(elem!1, s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[437, 427, 328])).
% 1.04/1.27 tff(439,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.04/1.27 tff(440,plain,
% 1.04/1.27 ((elem!1 = z) <=> (z = elem!1)),
% 1.04/1.27 inference(commutativity,[status(thm)],[])).
% 1.04/1.27 tff(441,plain,
% 1.04/1.27 ((z = elem!1) <=> (elem!1 = z)),
% 1.04/1.27 inference(symmetry,[status(thm)],[440])).
% 1.04/1.27 tff(442,assumption,(z = elem!1), introduced(assumption)).
% 1.04/1.27 tff(443,plain,
% 1.04/1.27 (elem!1 = z),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[442, 441])).
% 1.04/1.27 tff(444,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[439, 443])).
% 1.04/1.27 tff(445,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(446,plain,
% 1.04/1.27 (~(z = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[445, 439])).
% 1.04/1.27 tff(447,plain,
% 1.04/1.27 (b(s(s(s(s(z)))), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[247, 240])).
% 1.04/1.27 tff(448,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.04/1.27 tff(449,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(450,plain,
% 1.04/1.27 (((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(451,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[450])).
% 1.04/1.27 tff(452,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[451, 449])).
% 1.04/1.27 tff(453,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(454,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.04/1.27 tff(455,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[454, 77, 448, 66, 428])).
% 1.04/1.27 tff(456,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(457,plain,
% 1.04/1.27 (~r(s(s(z)), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[456, 26, 448])).
% 1.04/1.27 tff(458,plain,
% 1.04/1.27 (s(s(z)) = elem!1),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[426, 457, 1])).
% 1.04/1.27 tff(459,plain,
% 1.04/1.27 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(460,plain,
% 1.04/1.27 (inj_0(s(elem!1)) = elem!1),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[459, 36])).
% 1.04/1.27 tff(461,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.04/1.27 tff(462,plain,
% 1.04/1.27 (elem!1 = s(elem!1)),
% 1.04/1.27 inference(symmetry,[status(thm)],[461])).
% 1.04/1.27 tff(463,plain,
% 1.04/1.27 (s(s(z)) = s(elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[370, 462])).
% 1.04/1.27 tff(464,plain,
% 1.04/1.27 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[463])).
% 1.04/1.27 tff(465,plain,
% 1.04/1.27 (s(z) = elem!1),
% 1.04/1.27 inference(transitivity,[status(thm)],[44, 464, 460])).
% 1.04/1.27 tff(466,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.04/1.27 tff(467,plain,
% 1.04/1.27 (elem!1 = s(z)),
% 1.04/1.27 inference(symmetry,[status(thm)],[466])).
% 1.04/1.27 tff(468,plain,
% 1.04/1.27 (s(elem!1) = s(s(z))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[467])).
% 1.04/1.27 tff(469,plain,
% 1.04/1.27 (s(s(z)) = s(elem!1)),
% 1.04/1.27 inference(symmetry,[status(thm)],[468])).
% 1.04/1.27 tff(470,plain,
% 1.04/1.27 (elem!1 = s(s(z))),
% 1.04/1.27 inference(symmetry,[status(thm)],[370])).
% 1.04/1.27 tff(471,plain,
% 1.04/1.27 (s(z) = s(elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[466, 470, 469])).
% 1.04/1.27 tff(472,plain,
% 1.04/1.27 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[471])).
% 1.04/1.27 tff(473,plain,
% 1.04/1.27 (z = inj_0(s(z))),
% 1.04/1.27 inference(symmetry,[status(thm)],[47])).
% 1.04/1.27 tff(474,plain,
% 1.04/1.27 (z = elem!1),
% 1.04/1.27 inference(transitivity,[status(thm)],[473, 472, 460])).
% 1.04/1.27 tff(475,plain,
% 1.04/1.27 ((s(z) = z) <=> (elem!1 = z)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[466])).
% 1.04/1.27 tff(476,plain,
% 1.04/1.27 ((s(z) = z) <=> (z = elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[475, 440])).
% 1.04/1.27 tff(477,plain,
% 1.04/1.27 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[476])).
% 1.04/1.27 tff(478,plain,
% 1.04/1.27 (~(z = elem!1)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[206, 477])).
% 1.04/1.27 tff(479,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[478, 474])).
% 1.04/1.27 tff(480,plain,((~(s(s(z)) = elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(481,plain,
% 1.04/1.27 (~(s(z) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[480, 370])).
% 1.04/1.27 tff(482,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[481, 465])).
% 1.04/1.27 tff(483,plain,((~(s(elem!1) = elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(484,plain,
% 1.04/1.27 (~(s(elem!1) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[483, 458])).
% 1.04/1.27 tff(485,plain,
% 1.04/1.27 (s(s(s(z))) = s(elem!1)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[458])).
% 1.04/1.27 tff(486,plain,
% 1.04/1.27 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[485])).
% 1.04/1.27 tff(487,plain,
% 1.04/1.27 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[486])).
% 1.04/1.27 tff(488,plain,
% 1.04/1.27 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[487])).
% 1.04/1.27 tff(489,plain,
% 1.04/1.27 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[488])).
% 1.04/1.27 tff(490,plain,
% 1.04/1.27 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[458])).
% 1.04/1.27 tff(491,plain,
% 1.04/1.27 (r(elem!1, s(s(s(s(z)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[328, 490])).
% 1.04/1.27 tff(492,plain,
% 1.04/1.27 (r(elem!1, s(s(elem!1)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[491, 489])).
% 1.04/1.27 tff(493,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.27 tff(494,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.27 tff(495,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(496,plain,
% 1.04/1.27 (((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(497,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[496])).
% 1.04/1.27 tff(498,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[497, 495])).
% 1.04/1.27 tff(499,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(500,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.04/1.27 tff(501,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[500, 77, 448, 494, 493])).
% 1.04/1.27 tff(502,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(503,plain,
% 1.04/1.27 (~r(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[502, 492, 448])).
% 1.04/1.27 tff(504,plain,
% 1.04/1.27 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.04/1.27 inference(commutativity,[status(thm)],[])).
% 1.04/1.27 tff(505,plain,
% 1.04/1.27 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[504])).
% 1.04/1.27 tff(506,plain,
% 1.04/1.27 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[505])).
% 1.04/1.27 tff(507,plain,
% 1.04/1.27 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(508,plain,
% 1.04/1.27 (~(s(s(elem!1)) = z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[507, 9])).
% 1.04/1.27 tff(509,plain,
% 1.04/1.27 (~(z = s(s(elem!1)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[508, 506])).
% 1.04/1.27 tff(510,plain,
% 1.04/1.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(511,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(512,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.04/1.27 tff(513,plain,
% 1.04/1.27 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[512, 21])).
% 1.04/1.27 tff(514,plain,
% 1.04/1.27 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[513, 509])).
% 1.04/1.27 tff(515,plain,
% 1.04/1.27 (b(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[514, 503])).
% 1.04/1.27 tff(516,plain,
% 1.04/1.27 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[486])).
% 1.04/1.27 tff(517,plain,
% 1.04/1.27 (b(s(s(elem!1)), z)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[254, 516])).
% 1.04/1.27 tff(518,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.04/1.27 tff(519,plain,
% 1.04/1.27 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(520,plain,
% 1.04/1.27 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[519, 36])).
% 1.04/1.27 tff(521,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.04/1.27 tff(522,plain,
% 1.04/1.27 (elem!1 = s(s(elem!1))),
% 1.04/1.27 inference(symmetry,[status(thm)],[521])).
% 1.04/1.27 tff(523,plain,
% 1.04/1.27 (s(s(z)) = s(s(elem!1))),
% 1.04/1.27 inference(transitivity,[status(thm)],[370, 522])).
% 1.04/1.27 tff(524,plain,
% 1.04/1.27 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[523])).
% 1.04/1.27 tff(525,plain,
% 1.04/1.27 (s(z) = s(elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[44, 524, 520])).
% 1.04/1.27 tff(526,plain,
% 1.04/1.27 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[525])).
% 1.04/1.27 tff(527,plain,
% 1.04/1.27 (z = elem!1),
% 1.04/1.27 inference(transitivity,[status(thm)],[473, 526, 460])).
% 1.04/1.27 tff(528,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[518, 527])).
% 1.04/1.27 tff(529,plain,((~(s(s(z)) = elem!1)) | (z = elem!1) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(530,plain,
% 1.04/1.27 (~(s(s(elem!1)) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[529, 458, 518])).
% 1.04/1.27 tff(531,plain,
% 1.04/1.27 (z = elem!1),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[404, 440])).
% 1.04/1.27 tff(532,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[518, 531])).
% 1.04/1.27 tff(533,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(534,plain,
% 1.04/1.27 (~(elem!1 = z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[533, 518])).
% 1.04/1.27 tff(535,plain,
% 1.04/1.27 (b(s(s(z)), z) <=> b(elem!1, z)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[370])).
% 1.04/1.27 tff(536,plain,
% 1.04/1.27 (b(elem!1, z) <=> b(s(s(z)), z)),
% 1.04/1.27 inference(symmetry,[status(thm)],[535])).
% 1.04/1.27 tff(537,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.04/1.27 tff(538,plain,
% 1.04/1.27 (b(s(s(z)), z)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[537, 536])).
% 1.04/1.27 tff(539,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2, 538])).
% 1.04/1.27 tff(540,plain,((~(s(s(z)) = elem!1)) | b(s(s(z)), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(541,plain,
% 1.04/1.27 (~b(elem!1, z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[540, 458, 2])).
% 1.04/1.27 tff(542,plain,
% 1.04/1.27 (((~![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))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(543,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(544,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.04/1.27 tff(545,plain,
% 1.04/1.27 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[544, 21])).
% 1.04/1.27 tff(546,plain,
% 1.04/1.27 (r(elem!1, z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[545, 541, 534])).
% 1.04/1.27 tff(547,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 1.04/1.27 tff(548,plain,
% 1.04/1.27 (elem!1 = s(s(s(s(s(z)))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[547])).
% 1.04/1.27 tff(549,plain,
% 1.04/1.27 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[370, 548])).
% 1.04/1.27 tff(550,plain,
% 1.04/1.27 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[549])).
% 1.04/1.27 tff(551,plain,
% 1.04/1.27 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[550])).
% 1.04/1.27 tff(552,plain,
% 1.04/1.27 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(553,plain,
% 1.04/1.27 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[552, 36])).
% 1.04/1.27 tff(554,plain,
% 1.04/1.27 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[553])).
% 1.04/1.27 tff(555,plain,
% 1.04/1.27 (s(s(s(z))) = s(elem!1)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[370])).
% 1.04/1.27 tff(556,plain,
% 1.04/1.27 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[555])).
% 1.04/1.27 tff(557,plain,
% 1.04/1.27 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[556])).
% 1.04/1.27 tff(558,plain,
% 1.04/1.27 (s(s(elem!1)) = s(z)),
% 1.04/1.27 inference(transitivity,[status(thm)],[557, 554, 551, 43])).
% 1.04/1.27 tff(559,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.04/1.27 tff(560,plain,
% 1.04/1.27 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[559])).
% 1.04/1.27 tff(561,plain,
% 1.04/1.27 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[520])).
% 1.04/1.27 tff(562,plain,
% 1.04/1.27 (s(elem!1) = z),
% 1.04/1.27 inference(transitivity,[status(thm)],[561, 560, 47])).
% 1.04/1.27 tff(563,plain,
% 1.04/1.27 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(564,plain,
% 1.04/1.27 (~(s(elem!1) = z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[563, 9])).
% 1.04/1.27 tff(565,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[564, 562])).
% 1.04/1.27 tff(566,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(567,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[566, 558])).
% 1.04/1.27 tff(568,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(569,plain,
% 1.04/1.27 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[568, 370])).
% 1.04/1.27 tff(570,plain,
% 1.04/1.27 (~(s(elem!1) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[483, 370])).
% 1.04/1.27 tff(571,plain,
% 1.04/1.27 (~r(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[502, 493, 448])).
% 1.04/1.27 tff(572,plain,
% 1.04/1.27 (b(z, s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[514, 571])).
% 1.04/1.27 tff(573,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.04/1.27 tff(574,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.04/1.27 tff(575,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.04/1.27 tff(576,plain,
% 1.04/1.27 (s(elem!1) = s(s(s(z)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[555])).
% 1.04/1.27 tff(577,plain,
% 1.04/1.27 ((s(elem!1) = s(z)) <=> (s(s(s(z))) = s(z))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[576])).
% 1.04/1.27 tff(578,plain,
% 1.04/1.27 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.04/1.27 inference(symmetry,[status(thm)],[577])).
% 1.04/1.27 tff(579,plain,
% 1.04/1.27 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[578])).
% 1.04/1.27 tff(580,plain,
% 1.04/1.27 (~(s(elem!1) = s(z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[135, 579])).
% 1.04/1.27 tff(581,plain,
% 1.04/1.27 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[576])).
% 1.04/1.27 tff(582,plain,
% 1.04/1.27 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[581])).
% 1.04/1.27 tff(583,plain,
% 1.04/1.27 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[556, 555])).
% 1.04/1.27 tff(584,plain,
% 1.04/1.27 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[583])).
% 1.04/1.27 tff(585,plain,
% 1.04/1.27 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[576])).
% 1.04/1.27 tff(586,plain,
% 1.04/1.27 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.04/1.27 inference(symmetry,[status(thm)],[585])).
% 1.04/1.27 tff(587,plain,
% 1.04/1.27 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.04/1.27 inference(commutativity,[status(thm)],[])).
% 1.04/1.27 tff(588,plain,
% 1.04/1.27 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[587, 586, 584])).
% 1.04/1.27 tff(589,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.04/1.27 tff(590,plain,
% 1.04/1.27 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.04/1.27 tff(591,plain,
% 1.04/1.27 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.04/1.27 inference(commutativity,[status(thm)],[])).
% 1.04/1.27 tff(592,plain,
% 1.04/1.27 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[370])).
% 1.04/1.27 tff(593,plain,
% 1.04/1.27 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[592, 591])).
% 1.04/1.27 tff(594,plain,
% 1.04/1.27 ((s(s(s(z))) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[593])).
% 1.04/1.27 tff(595,plain,
% 1.04/1.27 ((s(elem!1) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[576])).
% 1.04/1.27 tff(596,plain,
% 1.04/1.27 ((s(elem!1) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[595, 594])).
% 1.04/1.27 tff(597,plain,
% 1.04/1.27 ((~(s(elem!1) = elem!1)) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[596])).
% 1.04/1.27 tff(598,plain,
% 1.04/1.27 (~(s(s(z)) = s(s(s(z))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[570, 597])).
% 1.04/1.27 tff(599,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.04/1.27 tff(600,plain,
% 1.04/1.27 (s(s(s(z))) = s(s(s(s(z))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[599])).
% 1.04/1.27 tff(601,plain,
% 1.04/1.27 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[600])).
% 1.04/1.27 tff(602,plain,
% 1.04/1.27 (s(s(z)) = s(s(s(z)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[132, 601, 127])).
% 1.04/1.27 tff(603,assumption,(~(s(s(z)) = s(s(s(z))))), introduced(assumption)).
% 1.04/1.27 tff(604,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[603, 602])).
% 1.04/1.27 tff(605,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(606,plain,
% 1.04/1.27 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[605, 598])).
% 1.04/1.27 tff(607,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[606, 590])).
% 1.04/1.27 tff(608,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(609,plain,
% 1.04/1.27 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[608, 370])).
% 1.04/1.27 tff(610,plain,
% 1.04/1.27 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[555])).
% 1.04/1.27 tff(611,plain,
% 1.04/1.27 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[610])).
% 1.04/1.27 tff(612,plain,
% 1.04/1.27 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[611])).
% 1.04/1.27 tff(613,plain,
% 1.04/1.27 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[576])).
% 1.04/1.27 tff(614,plain,
% 1.04/1.27 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.04/1.27 inference(symmetry,[status(thm)],[613])).
% 1.04/1.27 tff(615,plain,
% 1.04/1.27 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[614])).
% 1.04/1.27 tff(616,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(617,plain,
% 1.04/1.27 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.04/1.27 inference(symmetry,[status(thm)],[416])).
% 1.04/1.27 tff(618,plain,
% 1.04/1.27 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[617])).
% 1.04/1.27 tff(619,plain,
% 1.04/1.27 (~(elem!1 = s(z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[481, 618])).
% 1.04/1.27 tff(620,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.04/1.27 tff(621,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(622,plain,
% 1.04/1.27 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(623,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[622])).
% 1.04/1.27 tff(624,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[623, 621])).
% 1.04/1.27 tff(625,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(626,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.04/1.27 tff(627,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[626, 77, 575, 155, 620])).
% 1.04/1.27 tff(628,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(629,plain,
% 1.04/1.27 (~r(elem!1, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[628, 155, 575])).
% 1.04/1.27 tff(630,plain,
% 1.04/1.27 (((~![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)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(631,plain,
% 1.04/1.27 ((~![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)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(632,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.04/1.27 tff(633,plain,
% 1.04/1.27 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[632, 21])).
% 1.04/1.27 tff(634,plain,
% 1.04/1.27 (b(elem!1, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[633, 629, 619])).
% 1.04/1.27 tff(635,plain,
% 1.04/1.27 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[555])).
% 1.04/1.27 tff(636,plain,
% 1.04/1.27 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[370])).
% 1.04/1.27 tff(637,plain,
% 1.04/1.27 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[636])).
% 1.04/1.27 tff(638,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(639,plain,
% 1.04/1.27 (r(s(s(s(z))), s(s(z)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[638, 637])).
% 1.04/1.27 tff(640,plain,
% 1.04/1.27 (~r(s(s(s(z))), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[85, 639, 66])).
% 1.04/1.27 tff(641,plain,
% 1.04/1.27 (b(s(s(s(z))), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[63, 640])).
% 1.04/1.27 tff(642,plain,
% 1.04/1.27 (b(s(elem!1), z)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[641, 635])).
% 1.04/1.27 tff(643,plain,
% 1.04/1.27 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[581])).
% 1.04/1.27 tff(644,plain,
% 1.04/1.27 (r(s(elem!1), elem!1)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[638, 614])).
% 1.04/1.27 tff(645,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(646,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[645, 644])).
% 1.04/1.27 tff(647,plain,(r(s(elem!1), elem!1) | (~r(s(s(s(z))), elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(648,plain,
% 1.04/1.27 (r(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[647, 638, 370])).
% 1.04/1.27 tff(649,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.27 tff(650,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(651,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(652,plain,
% 1.04/1.28 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(653,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[652])).
% 1.04/1.28 tff(654,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[653, 651])).
% 1.04/1.28 tff(655,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(656,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.04/1.28 tff(657,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[656, 77, 575, 493, 650, 649])).
% 1.04/1.28 tff(658,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(659,plain,
% 1.04/1.28 (~r(s(elem!1), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[658, 648, 493, 575])).
% 1.04/1.28 tff(660,plain,
% 1.04/1.28 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[659, 643])).
% 1.04/1.28 tff(661,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(662,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(663,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.04/1.28 tff(664,plain,
% 1.04/1.28 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[663, 21])).
% 1.04/1.28 tff(665,plain,
% 1.04/1.28 (b(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[664, 660, 609])).
% 1.04/1.28 tff(666,plain,
% 1.04/1.28 (b(s(elem!1), s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[665, 610])).
% 1.04/1.28 tff(667,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.04/1.28 tff(668,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.28 tff(669,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(670,plain,
% 1.04/1.28 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(671,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[670])).
% 1.04/1.28 tff(672,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[671, 669])).
% 1.04/1.28 tff(673,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(674,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.04/1.28 tff(675,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[674, 116, 616, 668, 667, 666, 642])).
% 1.04/1.28 tff(676,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~(s(s(z)) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(677,plain,
% 1.04/1.28 (~r(s(s(s(z))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[676, 634, 572, 616, 370, 493, 575, 66])).
% 1.04/1.28 tff(678,plain,
% 1.04/1.28 (~r(s(elem!1), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[677, 615])).
% 1.04/1.28 tff(679,plain,
% 1.04/1.28 (((~![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))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(680,plain,
% 1.04/1.28 ((~![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))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(681,plain,
% 1.04/1.28 ((~![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)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[680, 679])).
% 1.04/1.28 tff(682,plain,
% 1.04/1.28 (b(s(elem!1), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[681, 21, 570, 678])).
% 1.04/1.28 tff(683,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(684,plain,
% 1.04/1.28 (((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(685,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[684])).
% 1.04/1.28 tff(686,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.04/1.28 inference(transitivity,[status(thm)],[685, 683])).
% 1.04/1.28 tff(687,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(688,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.04/1.28 tff(689,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[688, 77, 448, 360, 155])).
% 1.04/1.28 tff(690,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(691,plain,
% 1.04/1.28 (~r(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[690, 155, 448])).
% 1.04/1.28 tff(692,plain,
% 1.04/1.28 (b(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[357, 691, 481])).
% 1.04/1.28 tff(693,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(694,plain,
% 1.04/1.28 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(695,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[694])).
% 1.04/1.28 tff(696,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.28 inference(transitivity,[status(thm)],[695, 693])).
% 1.04/1.28 tff(697,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(698,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[697, 696])).
% 1.04/1.28 tff(699,plain,
% 1.04/1.28 (~b(s(elem!1), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[698, 116, 616, 692, 634, 682])).
% 1.04/1.28 tff(700,plain,
% 1.04/1.28 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[699, 612])).
% 1.04/1.28 tff(701,plain,
% 1.04/1.28 (r(s(s(s(z))), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[664, 700, 609])).
% 1.04/1.28 tff(702,plain,
% 1.04/1.28 (r(s(elem!1), s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[701, 582])).
% 1.04/1.28 tff(703,plain,
% 1.04/1.28 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.04/1.28 inference(commutativity,[status(thm)],[])).
% 1.04/1.28 tff(704,plain,
% 1.04/1.28 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.04/1.28 inference(symmetry,[status(thm)],[703])).
% 1.04/1.28 tff(705,plain,
% 1.04/1.28 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[704])).
% 1.04/1.28 tff(706,plain,
% 1.04/1.28 (~(s(z) = s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[566, 705])).
% 1.04/1.28 tff(707,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(708,plain,
% 1.04/1.28 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(709,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[708])).
% 1.04/1.28 tff(710,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[709, 707])).
% 1.04/1.28 tff(711,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(712,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[711, 710])).
% 1.04/1.28 tff(713,plain,
% 1.04/1.28 (~b(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[712, 116, 616, 692, 634])).
% 1.04/1.28 tff(714,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(715,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(716,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[715, 714])).
% 1.04/1.28 tff(717,plain,
% 1.04/1.28 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[716, 21, 713])).
% 1.04/1.28 tff(718,plain,
% 1.04/1.28 (r(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[717, 706])).
% 1.04/1.28 tff(719,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(720,plain,
% 1.04/1.28 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(721,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[720])).
% 1.04/1.28 tff(722,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[721, 719])).
% 1.04/1.28 tff(723,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(724,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[723, 722])).
% 1.04/1.28 tff(725,plain,
% 1.04/1.28 (~r(s(elem!1), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[724, 77, 155, 718, 702])).
% 1.04/1.28 tff(726,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(727,plain,
% 1.04/1.28 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(728,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[727])).
% 1.04/1.28 tff(729,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[728, 726])).
% 1.04/1.28 tff(730,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(731,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[730, 729])).
% 1.04/1.28 tff(732,plain,
% 1.04/1.28 (~b(s(elem!1), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[731, 116, 692, 634, 682])).
% 1.04/1.28 tff(733,plain,
% 1.04/1.28 (((~![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)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(734,plain,
% 1.04/1.28 ((~![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)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(735,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.04/1.28 tff(736,plain,
% 1.04/1.28 ((s(elem!1) = s(z)) | r(s(elem!1), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[735, 21, 732])).
% 1.04/1.28 tff(737,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[736, 725, 580])).
% 1.04/1.28 tff(738,plain,((~r(s(z), z)) | (~(s(s(z)) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(739,plain,
% 1.04/1.28 (~b(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[738, 155, 370, 493, 575, 66, 448])).
% 1.04/1.28 tff(740,plain,
% 1.04/1.28 (((~![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))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(741,plain,
% 1.04/1.28 ((~![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))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(742,plain,
% 1.04/1.28 ((~![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)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[741, 740])).
% 1.04/1.28 tff(743,plain,
% 1.04/1.28 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[742, 21])).
% 1.04/1.28 tff(744,plain,
% 1.04/1.28 (r(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[743, 739, 574])).
% 1.04/1.28 tff(745,plain,
% 1.04/1.28 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 1.04/1.28 inference(transitivity,[status(thm)],[613, 637])).
% 1.04/1.28 tff(746,plain,
% 1.04/1.28 (r(s(s(s(z))), s(s(z)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[650, 745])).
% 1.04/1.28 tff(747,plain,
% 1.04/1.28 (~r(s(s(s(z))), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[85, 746, 66])).
% 1.04/1.28 tff(748,plain,
% 1.04/1.28 (b(s(s(s(z))), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[63, 747])).
% 1.04/1.28 tff(749,plain,
% 1.04/1.28 (b(s(elem!1), z)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[748, 635])).
% 1.04/1.28 tff(750,plain,
% 1.04/1.28 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[583])).
% 1.04/1.28 tff(751,plain,
% 1.04/1.28 (~(s(s(elem!1)) = s(elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[606, 750])).
% 1.04/1.28 tff(752,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(753,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(754,plain,
% 1.04/1.29 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(755,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[754])).
% 1.04/1.29 tff(756,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[755, 753])).
% 1.04/1.29 tff(757,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(758,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[757, 756])).
% 1.04/1.29 tff(759,plain,
% 1.04/1.29 (~r(s(s(elem!1)), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[758, 77, 752, 650])).
% 1.04/1.29 tff(760,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.04/1.29 tff(761,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.04/1.29 tff(762,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.04/1.29 tff(763,plain,
% 1.04/1.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(764,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(765,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[764, 763])).
% 1.04/1.29 tff(766,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[765, 21, 762, 761, 760])).
% 1.04/1.29 tff(767,plain,(r(s(s(elem!1)), s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(768,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[767, 759, 751])).
% 1.04/1.29 tff(769,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(770,plain,
% 1.04/1.29 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(771,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[770])).
% 1.04/1.29 tff(772,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[771, 769])).
% 1.04/1.29 tff(773,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(774,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.04/1.29 tff(775,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[774, 116, 668, 573, 768, 749])).
% 1.04/1.29 tff(776,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~(s(s(z)) = elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(777,plain,
% 1.04/1.29 (~r(s(elem!1), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[776, 744, 573, 370, 66, 572])).
% 1.04/1.29 tff(778,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.04/1.29 tff(779,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(780,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[681, 21, 779, 778, 645])).
% 1.04/1.29 tff(781,plain,(r(s(elem!1), elem!1) | b(s(elem!1), elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(782,plain,
% 1.04/1.29 (b(s(elem!1), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[781, 777, 570])).
% 1.04/1.29 tff(783,plain,
% 1.04/1.29 (~r(s(z), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[628, 620, 575])).
% 1.04/1.29 tff(784,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(785,plain,
% 1.04/1.29 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(786,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[785])).
% 1.04/1.29 tff(787,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[786, 784])).
% 1.04/1.29 tff(788,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(789,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[788, 787])).
% 1.04/1.29 tff(790,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[789, 77, 448, 293, 620])).
% 1.04/1.29 tff(791,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(792,plain,
% 1.04/1.29 (~r(z, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[791, 620, 448])).
% 1.04/1.29 tff(793,plain,
% 1.04/1.29 (b(z, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[289, 792])).
% 1.04/1.29 tff(794,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.04/1.29 tff(795,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(796,plain,
% 1.04/1.29 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(797,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[796])).
% 1.04/1.29 tff(798,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[797, 795])).
% 1.04/1.29 tff(799,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(800,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.04/1.29 tff(801,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[800, 77, 794, 620, 493])).
% 1.04/1.29 tff(802,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(803,plain,
% 1.04/1.29 (~r(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[802, 620, 493])).
% 1.04/1.29 tff(804,plain,
% 1.04/1.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(805,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(806,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[805, 804])).
% 1.04/1.29 tff(807,plain,
% 1.04/1.29 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[806, 21])).
% 1.04/1.29 tff(808,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[807, 566])).
% 1.04/1.29 tff(809,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[808, 803])).
% 1.04/1.29 tff(810,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(811,plain,
% 1.04/1.29 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(812,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[811])).
% 1.04/1.29 tff(813,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[812, 810])).
% 1.04/1.29 tff(814,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(815,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[814, 813])).
% 1.04/1.29 tff(816,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[815, 116, 809, 270, 572, 793, 573])).
% 1.04/1.29 tff(817,plain,((~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(818,plain,
% 1.04/1.29 (~b(s(z), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[817, 620, 573, 493, 448])).
% 1.04/1.29 tff(819,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[210, 818, 783])).
% 1.04/1.29 tff(820,plain,((~r(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(821,plain,
% 1.04/1.29 (~r(elem!1, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[820, 573, 493, 448, 575])).
% 1.04/1.29 tff(822,plain,
% 1.04/1.29 (b(elem!1, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[633, 821, 619])).
% 1.04/1.29 tff(823,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.29 tff(824,plain,
% 1.04/1.29 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[823])).
% 1.04/1.29 tff(825,plain,
% 1.04/1.29 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.04/1.29 inference(symmetry,[status(thm)],[824])).
% 1.04/1.29 tff(826,plain,
% 1.04/1.29 (s(s(elem!1)) = z),
% 1.04/1.29 inference(transitivity,[status(thm)],[557, 554, 825, 47])).
% 1.04/1.29 tff(827,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[508, 826])).
% 1.04/1.29 tff(828,plain,((~(s(z) = s(s(s(s(s(z))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(829,plain,
% 1.04/1.29 (~(s(z) = s(s(s(s(s(z))))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[828, 370])).
% 1.04/1.29 tff(830,assumption,(s(elem!1) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.29 tff(831,plain,
% 1.04/1.29 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.04/1.29 inference(symmetry,[status(thm)],[830])).
% 1.04/1.29 tff(832,plain,
% 1.04/1.29 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[831])).
% 1.04/1.29 tff(833,plain,
% 1.04/1.29 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[576])).
% 1.04/1.29 tff(834,plain,
% 1.04/1.29 (s(s(elem!1)) = elem!1),
% 1.04/1.29 inference(transitivity,[status(thm)],[833, 554, 832, 460])).
% 1.04/1.29 tff(835,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[574, 834])).
% 1.04/1.29 tff(836,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (s(s(elem!1)) = elem!1) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(837,plain,
% 1.04/1.29 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[836, 574, 370])).
% 1.04/1.29 tff(838,plain,
% 1.04/1.29 (~b(s(elem!1), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[731, 116, 692, 822, 782])).
% 1.04/1.29 tff(839,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.04/1.29 tff(840,plain,
% 1.04/1.29 (s(s(s(z))) = s(z)),
% 1.04/1.29 inference(transitivity,[status(thm)],[555, 839])).
% 1.04/1.29 tff(841,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[135, 840])).
% 1.04/1.29 tff(842,plain,((~(s(elem!1) = s(z))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(843,plain,
% 1.04/1.29 (~(s(elem!1) = s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[842, 370])).
% 1.04/1.29 tff(844,plain,
% 1.04/1.29 (r(s(elem!1), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[735, 21, 843, 838])).
% 1.04/1.29 tff(845,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(846,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(847,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(848,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(849,plain,
% 1.04/1.29 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(850,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[849])).
% 1.04/1.29 tff(851,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[850, 848])).
% 1.04/1.29 tff(852,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(853,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.04/1.29 tff(854,plain,
% 1.04/1.29 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[853, 116, 847, 667, 846, 845])).
% 1.04/1.29 tff(855,assumption,(~(s(elem!1) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.04/1.29 tff(856,plain,
% 1.04/1.29 (((~![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)))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(857,plain,
% 1.04/1.29 ((~![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)))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(858,plain,
% 1.04/1.29 ((~![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))))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.04/1.29 tff(859,plain,
% 1.04/1.29 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[858, 21, 855, 854])).
% 1.04/1.29 tff(860,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(861,plain,
% 1.04/1.29 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(862,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[861])).
% 1.04/1.29 tff(863,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.04/1.29 inference(transitivity,[status(thm)],[862, 860])).
% 1.04/1.29 tff(864,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(865,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.04/1.29 tff(866,plain,
% 1.04/1.29 (~b(s(z), s(s(s(s(s(z))))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[865, 116, 847, 667, 845])).
% 1.04/1.29 tff(867,assumption,(~(s(z) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.04/1.29 tff(868,plain,
% 1.04/1.29 (((~![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)))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(869,plain,
% 1.04/1.29 ((~![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)))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(870,plain,
% 1.04/1.29 ((~![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))))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[869, 868])).
% 1.04/1.29 tff(871,plain,
% 1.04/1.29 (r(s(z), s(s(s(s(s(z))))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[870, 21, 867, 866])).
% 1.04/1.29 tff(872,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.04/1.29 tff(873,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(874,plain,
% 1.04/1.29 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(875,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z)))))),
% 1.04/1.30 inference(monotonicity,[status(thm)],[874])).
% 1.04/1.30 tff(876,plain,
% 1.04/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))),
% 1.04/1.30 inference(transitivity,[status(thm)],[875, 873])).
% 1.04/1.30 tff(877,plain,
% 1.04/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))))),
% 1.04/1.30 inference(quant_inst,[status(thm)],[])).
% 1.04/1.30 tff(878,plain,
% 1.04/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[877, 876])).
% 1.14/1.30 tff(879,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[878, 77, 872, 871, 859])).
% 1.14/1.30 tff(880,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(z) = s(s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(881,plain,
% 1.14/1.30 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[880, 844, 837, 829, 692, 822, 782])).
% 1.14/1.30 tff(882,plain,
% 1.14/1.30 (((~![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))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(883,plain,
% 1.14/1.30 ((~![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))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(884,plain,
% 1.14/1.30 ((~![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)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.14/1.30 tff(885,plain,
% 1.14/1.30 ((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)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[884, 21])).
% 1.14/1.30 tff(886,plain,
% 1.14/1.30 (r(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[885, 881, 569])).
% 1.14/1.30 tff(887,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(888,plain,
% 1.14/1.30 (((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(889,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[888])).
% 1.14/1.30 tff(890,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[889, 887])).
% 1.14/1.30 tff(891,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(892,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.14/1.30 tff(893,plain,
% 1.14/1.30 (~r(s(s(s(s(s(z))))), z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[892, 77, 448, 886])).
% 1.14/1.30 tff(894,plain,
% 1.14/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(895,plain,
% 1.14/1.30 (~(s(s(s(s(s(z))))) = z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[894, 9])).
% 1.14/1.30 tff(896,plain,
% 1.14/1.30 (((~![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))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(897,plain,
% 1.14/1.30 ((~![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))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(898,plain,
% 1.14/1.30 ((~![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)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.14/1.30 tff(899,plain,
% 1.14/1.30 (b(s(s(s(s(s(z))))), z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[898, 21, 895, 893])).
% 1.14/1.30 tff(900,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(901,plain,
% 1.14/1.30 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(902,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[901])).
% 1.14/1.30 tff(903,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[902, 900])).
% 1.14/1.30 tff(904,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(905,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[904, 903])).
% 1.14/1.30 tff(906,plain,
% 1.14/1.30 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[905, 77, 744, 886])).
% 1.14/1.30 tff(907,assumption,(s(s(elem!1)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.30 tff(908,plain,
% 1.14/1.30 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[907])).
% 1.14/1.30 tff(909,plain,
% 1.14/1.30 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.14/1.30 inference(symmetry,[status(thm)],[908])).
% 1.14/1.30 tff(910,plain,
% 1.14/1.30 (s(s(elem!1)) = s(elem!1)),
% 1.14/1.30 inference(transitivity,[status(thm)],[557, 554, 909, 520])).
% 1.14/1.30 tff(911,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[751, 910])).
% 1.14/1.30 tff(912,plain,((~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(913,plain,
% 1.14/1.30 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[912, 370])).
% 1.14/1.30 tff(914,plain,
% 1.14/1.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(915,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(916,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.14/1.30 tff(917,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[916, 21, 913, 906])).
% 1.14/1.30 tff(918,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(919,plain,
% 1.14/1.30 (((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(920,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[919])).
% 1.14/1.30 tff(921,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[920, 918])).
% 1.14/1.30 tff(922,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(923,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[922, 921])).
% 1.14/1.30 tff(924,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[923, 116, 572, 573, 917, 899])).
% 1.14/1.30 tff(925,plain,((~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~(s(s(z)) = elem!1)) | (~r(s(s(z)), z)) | (s(s(elem!1)) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(926,plain,
% 1.14/1.30 (~r(s(z), z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[925, 517, 448, 458, 26, 530, 492, 546])).
% 1.14/1.30 tff(927,plain,
% 1.14/1.30 (b(s(z), z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[210, 926])).
% 1.14/1.30 tff(928,plain,
% 1.14/1.30 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[568, 458])).
% 1.14/1.30 tff(929,plain,
% 1.14/1.30 (~(s(z) = elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[480, 458])).
% 1.14/1.30 tff(930,plain,
% 1.14/1.30 (~(elem!1 = s(z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[929, 618])).
% 1.14/1.30 tff(931,plain,
% 1.14/1.30 (~r(elem!1, s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[820, 517, 492, 448, 546])).
% 1.14/1.30 tff(932,plain,
% 1.14/1.30 (b(elem!1, s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[633, 931, 930])).
% 1.14/1.30 tff(933,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(934,plain,
% 1.14/1.30 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(935,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[934])).
% 1.14/1.30 tff(936,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[935, 933])).
% 1.14/1.30 tff(937,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(938,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.14/1.30 tff(939,plain,
% 1.14/1.30 (~b(s(z), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[938, 116, 927, 515, 517])).
% 1.14/1.30 tff(940,plain,
% 1.14/1.30 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[716, 21, 939])).
% 1.14/1.30 tff(941,plain,
% 1.14/1.30 (r(s(z), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[940, 706])).
% 1.14/1.30 tff(942,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(943,plain,
% 1.14/1.30 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(944,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[943])).
% 1.14/1.30 tff(945,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[944, 942])).
% 1.14/1.30 tff(946,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(947,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[946, 945])).
% 1.14/1.30 tff(948,plain,
% 1.14/1.30 (~r(s(z), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[947, 77, 546, 492, 941])).
% 1.14/1.30 tff(949,plain,
% 1.14/1.30 (b(s(z), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[357, 948, 929])).
% 1.14/1.30 tff(950,plain,
% 1.14/1.30 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[912, 458])).
% 1.14/1.30 tff(951,plain,
% 1.14/1.30 (~(s(z) = s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[828, 458])).
% 1.14/1.30 tff(952,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.14/1.30 tff(953,assumption,(~(s(s(elem!1)) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.14/1.30 tff(954,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.14/1.30 tff(955,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(956,plain,
% 1.14/1.30 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(957,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[956])).
% 1.14/1.30 tff(958,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[957, 955])).
% 1.14/1.30 tff(959,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(960,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[959, 958])).
% 1.14/1.30 tff(961,plain,
% 1.14/1.30 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[960, 116, 616, 668, 573, 954])).
% 1.14/1.30 tff(962,plain,
% 1.14/1.30 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[916, 21, 953, 961])).
% 1.14/1.30 tff(963,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(964,plain,
% 1.14/1.30 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~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(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(965,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[964])).
% 1.14/1.30 tff(966,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[965, 963])).
% 1.14/1.31 tff(967,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(968,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[967, 966])).
% 1.14/1.31 tff(969,plain,
% 1.14/1.31 (~b(s(z), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[968, 116, 616, 270, 668, 954])).
% 1.14/1.31 tff(970,plain,
% 1.14/1.31 (r(s(z), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[870, 21, 867, 969])).
% 1.14/1.31 tff(971,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(972,plain,
% 1.14/1.31 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(973,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[972])).
% 1.14/1.31 tff(974,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[973, 971])).
% 1.14/1.31 tff(975,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(976,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.14/1.31 tff(977,plain,
% 1.14/1.31 (~b(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[976, 116, 270, 668, 573])).
% 1.14/1.31 tff(978,plain,
% 1.14/1.31 (r(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[808, 977])).
% 1.14/1.31 tff(979,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(980,plain,
% 1.14/1.31 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(981,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[980])).
% 1.14/1.31 tff(982,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[981, 979])).
% 1.14/1.31 tff(983,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(984,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[983, 982])).
% 1.14/1.31 tff(985,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[984, 77, 978, 970, 962])).
% 1.14/1.31 tff(986,plain,((~b(s(s(s(s(s(z))))), z)) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (s(z) = s(s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(987,plain,
% 1.14/1.31 (~b(s(s(s(s(s(z))))), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[986, 616, 867, 953, 668, 573, 270])).
% 1.14/1.31 tff(988,plain,
% 1.14/1.31 (r(s(s(s(s(s(z))))), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[898, 21, 895, 987])).
% 1.14/1.31 tff(989,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(990,plain,
% 1.14/1.31 (((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(991,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[990])).
% 1.14/1.31 tff(992,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[991, 989])).
% 1.14/1.31 tff(993,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(994,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.14/1.31 tff(995,plain,
% 1.14/1.31 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[994, 77, 575, 988])).
% 1.14/1.31 tff(996,plain,
% 1.14/1.31 (b(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[885, 995, 952])).
% 1.14/1.31 tff(997,plain,
% 1.14/1.31 (~b(s(z), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[865, 116, 847, 667, 996])).
% 1.14/1.31 tff(998,plain,
% 1.14/1.31 (r(s(z), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[870, 21, 867, 997])).
% 1.14/1.31 tff(999,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1000,plain,
% 1.14/1.31 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1001,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1000])).
% 1.14/1.31 tff(1002,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1001, 999])).
% 1.14/1.31 tff(1003,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1004,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 1.14/1.31 tff(1005,plain,
% 1.14/1.31 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1004, 116, 616, 847, 667, 996])).
% 1.14/1.31 tff(1006,plain,
% 1.14/1.31 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[916, 21, 953, 1005])).
% 1.14/1.31 tff(1007,plain,
% 1.14/1.31 (~b(s(z), s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[938, 116, 270, 668, 573])).
% 1.14/1.31 tff(1008,plain,
% 1.14/1.31 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[716, 21, 1007])).
% 1.14/1.31 tff(1009,plain,
% 1.14/1.31 (r(s(z), s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1008, 706])).
% 1.14/1.31 tff(1010,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1011,plain,
% 1.14/1.31 (((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1012,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1011])).
% 1.14/1.31 tff(1013,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1012, 1010])).
% 1.14/1.31 tff(1014,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1015,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 1.14/1.31 tff(1016,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1015, 77, 1009, 1006, 998])).
% 1.14/1.31 tff(1017,plain,((~b(s(s(elem!1)), elem!1)) | (s(z) = s(s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1018,plain,
% 1.14/1.31 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1017, 951, 950, 949, 932, 928, 546, 515, 517, 927])).
% 1.14/1.31 tff(1019,plain,
% 1.14/1.31 (r(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[743, 1018, 530])).
% 1.14/1.31 tff(1020,plain,
% 1.14/1.31 (~r(s(elem!1), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[776, 1019, 517, 458, 26, 515])).
% 1.14/1.31 tff(1021,plain,
% 1.14/1.31 (b(s(elem!1), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[781, 1020, 484])).
% 1.14/1.31 tff(1022,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.14/1.31 tff(1023,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[731, 116, 847, 667, 846, 1022])).
% 1.14/1.31 tff(1024,plain,((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1025,plain,
% 1.14/1.31 (~b(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1024, 949, 932, 1021])).
% 1.14/1.31 tff(1026,plain,
% 1.14/1.31 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[836, 530, 458])).
% 1.14/1.31 tff(1027,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.14/1.31 tff(1028,plain,
% 1.14/1.31 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[905, 77, 752, 1027])).
% 1.14/1.31 tff(1029,plain,
% 1.14/1.31 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[916, 21, 953, 1028])).
% 1.14/1.31 tff(1030,plain,
% 1.14/1.31 (~r(s(s(s(s(s(z))))), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[892, 77, 448, 1027])).
% 1.14/1.31 tff(1031,plain,
% 1.14/1.31 (b(s(s(s(s(s(z))))), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[898, 21, 895, 1030])).
% 1.14/1.31 tff(1032,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[923, 116, 668, 573, 1031, 1029])).
% 1.14/1.31 tff(1033,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1034,plain,
% 1.14/1.31 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1033, 515, 517, 950, 448, 1019])).
% 1.14/1.31 tff(1035,plain,
% 1.14/1.31 (b(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[885, 1034, 928])).
% 1.14/1.31 tff(1036,plain,
% 1.14/1.31 (~r(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[880, 1035, 1026, 951, 949, 932, 1021])).
% 1.14/1.31 tff(1037,plain,
% 1.14/1.31 (~(s(elem!1) = s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[842, 458])).
% 1.14/1.31 tff(1038,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[735, 21, 1037, 1036, 1025])).
% 1.14/1.31 tff(1039,plain,(b(s(s(z)), z) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (z = elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1040,plain,
% 1.14/1.31 (~r(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1039, 1, 2, 447, 328, 446])).
% 1.14/1.31 tff(1041,plain,
% 1.14/1.31 (((~![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))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1042,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1043,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 1.14/1.31 tff(1044,plain,
% 1.14/1.31 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1043, 21])).
% 1.14/1.31 tff(1045,plain,
% 1.14/1.31 (b(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1044, 1040, 446])).
% 1.14/1.31 tff(1046,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.14/1.31 tff(1047,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.14/1.31 tff(1048,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.14/1.31 tff(1049,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.31 tff(1050,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.14/1.31 tff(1051,plain,
% 1.14/1.31 (b(elem!1, z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[545, 439, 1050])).
% 1.14/1.31 tff(1052,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.14/1.31 tff(1053,plain,
% 1.14/1.31 (b(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1044, 446, 1052])).
% 1.14/1.31 tff(1054,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.31 tff(1055,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.14/1.31 tff(1056,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1057,plain,
% 1.14/1.31 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1058,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1057])).
% 1.14/1.31 tff(1059,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1058, 1056])).
% 1.14/1.31 tff(1060,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1061,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 1.14/1.31 tff(1062,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1061, 116, 1055, 537, 1054, 254])).
% 1.14/1.31 tff(1063,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1064,plain,
% 1.14/1.31 (~b(elem!1, s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1063, 1053, 254, 1051])).
% 1.14/1.31 tff(1065,plain,
% 1.14/1.31 (((~![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))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1066,plain,
% 1.14/1.31 ((~![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))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1067,plain,
% 1.14/1.31 ((~![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)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 1.14/1.31 tff(1068,plain,
% 1.14/1.31 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1067, 21])).
% 1.14/1.31 tff(1069,plain,
% 1.14/1.31 (elem!1 = s(s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1068, 1064, 1049])).
% 1.14/1.31 tff(1070,plain,
% 1.14/1.31 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1069])).
% 1.14/1.31 tff(1071,plain,
% 1.14/1.31 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1070])).
% 1.14/1.31 tff(1072,plain,
% 1.14/1.31 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.14/1.31 inference(symmetry,[status(thm)],[1071])).
% 1.14/1.31 tff(1073,plain,
% 1.14/1.31 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1072])).
% 1.14/1.31 tff(1074,plain,
% 1.14/1.31 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.14/1.31 inference(symmetry,[status(thm)],[1073])).
% 1.14/1.31 tff(1075,plain,
% 1.14/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1076,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1075, 36])).
% 1.14/1.32 tff(1077,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.32 tff(1078,plain,
% 1.14/1.32 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1077])).
% 1.14/1.32 tff(1079,plain,
% 1.14/1.32 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1078])).
% 1.14/1.32 tff(1080,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.14/1.32 tff(1081,plain,
% 1.14/1.32 (s(s(s(s(z)))) = elem!1),
% 1.14/1.32 inference(symmetry,[status(thm)],[1077])).
% 1.14/1.32 tff(1082,plain,
% 1.14/1.32 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1081, 1080, 1079])).
% 1.14/1.32 tff(1083,plain,
% 1.14/1.32 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1082])).
% 1.14/1.32 tff(1084,plain,
% 1.14/1.32 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[128, 1083, 1076])).
% 1.14/1.32 tff(1085,plain,
% 1.14/1.32 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1084])).
% 1.14/1.32 tff(1086,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1085])).
% 1.14/1.32 tff(1087,plain,
% 1.14/1.32 (s(s(s(s(z)))) = s(s(z))),
% 1.14/1.32 inference(transitivity,[status(thm)],[554, 1086, 38])).
% 1.14/1.32 tff(1088,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[141, 1087])).
% 1.14/1.32 tff(1089,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(z))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1090,plain,
% 1.14/1.32 ((~(elem!1 = s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1089, 137])).
% 1.14/1.32 tff(1091,plain,
% 1.14/1.32 (~(elem!1 = s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1090, 1069])).
% 1.14/1.32 tff(1092,plain,
% 1.14/1.32 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(1093,plain,
% 1.14/1.32 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1092])).
% 1.14/1.32 tff(1094,plain,
% 1.14/1.32 (elem!1 = s(s(elem!1))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[521, 1093])).
% 1.14/1.32 tff(1095,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.14/1.32 tff(1096,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1095, 1094])).
% 1.14/1.32 tff(1097,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1098,plain,
% 1.14/1.32 (~(s(s(elem!1)) = elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1097, 1091])).
% 1.14/1.32 tff(1099,plain,
% 1.14/1.32 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1071])).
% 1.14/1.32 tff(1100,plain,
% 1.14/1.32 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.14/1.32 inference(symmetry,[status(thm)],[1099])).
% 1.14/1.32 tff(1101,plain,
% 1.14/1.32 (s(s(s(s(z)))) = elem!1),
% 1.14/1.32 inference(symmetry,[status(thm)],[1069])).
% 1.14/1.32 tff(1102,plain,
% 1.14/1.32 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1101])).
% 1.14/1.32 tff(1103,plain,
% 1.14/1.32 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), elem!1)),
% 1.14/1.32 inference(transitivity,[status(thm)],[1102, 1100])).
% 1.14/1.32 tff(1104,plain,
% 1.14/1.32 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1103])).
% 1.14/1.32 tff(1105,plain,
% 1.14/1.32 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1101])).
% 1.14/1.32 tff(1106,plain,
% 1.14/1.32 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1105])).
% 1.14/1.32 tff(1107,plain,
% 1.14/1.32 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1069])).
% 1.14/1.32 tff(1108,plain,
% 1.14/1.32 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1107])).
% 1.14/1.32 tff(1109,plain,
% 1.14/1.32 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1108])).
% 1.14/1.32 tff(1110,plain,
% 1.14/1.32 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1069])).
% 1.14/1.32 tff(1111,plain,
% 1.14/1.32 (b(z, s(s(s(s(z)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1053, 1110])).
% 1.14/1.32 tff(1112,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1113,plain,
% 1.14/1.32 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1114,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1113])).
% 1.14/1.32 tff(1115,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1114, 1112])).
% 1.14/1.32 tff(1116,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1117,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 1.14/1.32 tff(1118,plain,
% 1.14/1.32 (~b(s(s(s(s(z)))), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1117, 116, 270, 28, 254, 1111])).
% 1.14/1.32 tff(1119,plain,
% 1.14/1.32 (~b(elem!1, s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1118, 1109])).
% 1.14/1.32 tff(1120,plain,
% 1.14/1.32 (r(elem!1, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[633, 1119, 1046])).
% 1.14/1.32 tff(1121,plain,
% 1.14/1.32 (r(s(s(s(s(z)))), s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1120, 1106])).
% 1.14/1.32 tff(1122,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1123,plain,
% 1.14/1.32 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1124,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1123])).
% 1.14/1.32 tff(1125,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.14/1.32 tff(1126,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1127,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.14/1.32 tff(1128,plain,
% 1.14/1.32 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1127, 77, 1047, 1121])).
% 1.14/1.32 tff(1129,plain,
% 1.14/1.32 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(1130,plain,
% 1.14/1.32 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1129])).
% 1.14/1.32 tff(1131,plain,
% 1.14/1.32 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1130])).
% 1.14/1.32 tff(1132,plain,
% 1.14/1.32 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[599])).
% 1.14/1.32 tff(1133,plain,
% 1.14/1.32 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1132, 599])).
% 1.14/1.32 tff(1134,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 1.14/1.32 tff(1135,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1134])).
% 1.14/1.32 tff(1136,plain,
% 1.14/1.32 (s(s(s(s(z)))) = s(s(z))),
% 1.14/1.32 inference(transitivity,[status(thm)],[554, 1135, 38])).
% 1.14/1.32 tff(1137,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[137, 1136])).
% 1.14/1.32 tff(1138,plain,(~(s(s(s(s(s(z))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1139,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1138, 1133])).
% 1.14/1.32 tff(1140,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1141,plain,
% 1.14/1.32 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1140, 1131])).
% 1.14/1.32 tff(1142,plain,
% 1.14/1.32 (((~![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))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1143,plain,
% 1.14/1.32 ((~![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))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1144,plain,
% 1.14/1.32 ((~![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)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.14/1.32 tff(1145,plain,
% 1.14/1.32 ((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)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1144, 21])).
% 1.14/1.32 tff(1146,plain,
% 1.14/1.32 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1145, 1141])).
% 1.14/1.32 tff(1147,plain,
% 1.14/1.32 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1146, 1128])).
% 1.14/1.32 tff(1148,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1149,plain,
% 1.14/1.32 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1150,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1149])).
% 1.14/1.32 tff(1151,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1150, 1148])).
% 1.14/1.32 tff(1152,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1153,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.14/1.32 tff(1154,plain,
% 1.14/1.32 (~b(z, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1153, 116, 28, 176, 1147, 1111])).
% 1.14/1.32 tff(1155,plain,
% 1.14/1.32 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[267, 21, 1154])).
% 1.14/1.32 tff(1156,plain,
% 1.14/1.32 (r(z, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1155, 253])).
% 1.14/1.32 tff(1157,plain,
% 1.14/1.32 (~r(z, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[301, 1156, 292])).
% 1.14/1.32 tff(1158,plain,
% 1.14/1.32 (b(z, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[289, 1157])).
% 1.14/1.32 tff(1159,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1160,plain,
% 1.14/1.32 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1161,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1160])).
% 1.14/1.32 tff(1162,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.14/1.32 tff(1163,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1164,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.14/1.32 tff(1165,plain,
% 1.14/1.32 (~b(z, s(s(z)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1164, 116, 270, 1158, 1048])).
% 1.14/1.32 tff(1166,plain,
% 1.14/1.32 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(1167,plain,
% 1.14/1.32 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1166])).
% 1.14/1.32 tff(1168,plain,
% 1.14/1.32 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1167])).
% 1.14/1.32 tff(1169,plain,
% 1.14/1.32 (~(z = s(s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[11, 1168])).
% 1.14/1.32 tff(1170,plain,
% 1.14/1.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1171,plain,
% 1.14/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1172,plain,
% 1.14/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.14/1.32 tff(1173,plain,
% 1.14/1.32 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1172, 21])).
% 1.14/1.32 tff(1174,plain,
% 1.14/1.32 (b(z, s(s(z))) | r(z, s(s(z)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1173, 1169])).
% 1.14/1.32 tff(1175,plain,
% 1.14/1.32 (r(z, s(s(z)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1174, 1165])).
% 1.14/1.32 tff(1176,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.32 tff(1177,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.32 tff(1178,plain,
% 1.14/1.32 (~b(z, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1153, 116, 28, 176, 1177, 1176])).
% 1.14/1.32 tff(1179,plain,
% 1.14/1.32 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[267, 21, 1178])).
% 1.14/1.32 tff(1180,plain,
% 1.14/1.32 (r(z, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1179, 253])).
% 1.14/1.32 tff(1181,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.32 tff(1182,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1183,plain,
% 1.14/1.32 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(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)))))) <=> ((~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(z))), 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))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1184,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1183])).
% 1.14/1.32 tff(1185,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1184, 1182])).
% 1.14/1.32 tff(1186,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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(s(s(s(z)))))), s(s(s(z))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1187,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.14/1.32 tff(1188,plain,
% 1.14/1.32 ((~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)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1187, 116, 28, 176, 1177])).
% 1.14/1.32 tff(1189,plain,
% 1.14/1.32 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1188, 1181])).
% 1.14/1.32 tff(1190,plain,
% 1.14/1.32 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(1191,plain,
% 1.14/1.32 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1190])).
% 1.14/1.32 tff(1192,assumption,(s(s(s(z))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.14/1.32 tff(1193,plain,
% 1.14/1.32 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1192])).
% 1.14/1.32 tff(1194,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1193])).
% 1.14/1.32 tff(1195,plain,
% 1.14/1.32 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1076])).
% 1.14/1.32 tff(1196,plain,
% 1.14/1.32 (s(s(s(s(s(z))))) = s(s(z))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1195, 1194, 38])).
% 1.14/1.32 tff(1197,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.14/1.32 tff(1198,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1197])).
% 1.14/1.32 tff(1199,plain,
% 1.14/1.32 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.33 inference(symmetry,[status(thm)],[1198])).
% 1.14/1.33 tff(1200,plain,
% 1.14/1.33 (s(z) = s(s(s(s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[44, 1199, 553])).
% 1.14/1.33 tff(1201,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[320, 1200])).
% 1.14/1.33 tff(1202,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1203,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1202, 1196])).
% 1.14/1.33 tff(1204,plain,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1205,plain,
% 1.14/1.33 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1204, 1191])).
% 1.14/1.33 tff(1206,plain,
% 1.14/1.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(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(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1207,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1208,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.14/1.33 tff(1209,plain,
% 1.14/1.33 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1208, 21])).
% 1.14/1.33 tff(1210,plain,
% 1.14/1.33 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1209, 1205])).
% 1.14/1.33 tff(1211,plain,
% 1.14/1.33 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1210, 1189])).
% 1.14/1.33 tff(1212,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.14/1.33 tff(1213,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1214,plain,
% 1.14/1.33 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, 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(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1215,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1214])).
% 1.14/1.33 tff(1216,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1215, 1213])).
% 1.14/1.33 tff(1217,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1218,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 1.14/1.33 tff(1219,plain,
% 1.14/1.33 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1218, 77, 1212, 1211, 1180])).
% 1.14/1.33 tff(1220,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1221,plain,
% 1.14/1.33 (((~b(s(s(s(z))), 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(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(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1222,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1221])).
% 1.14/1.33 tff(1223,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.14/1.33 tff(1224,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1225,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.14/1.33 tff(1226,plain,
% 1.14/1.33 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1225, 116, 28, 176, 1176])).
% 1.14/1.33 tff(1227,plain,
% 1.14/1.33 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1226, 1181])).
% 1.14/1.33 tff(1228,plain,
% 1.14/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1229,plain,
% 1.14/1.33 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1228, 9])).
% 1.14/1.33 tff(1230,plain,
% 1.14/1.33 (((~![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))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1231,plain,
% 1.14/1.33 ((~![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))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1232,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 1.14/1.33 tff(1233,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1232, 21, 1229, 1227, 1219])).
% 1.14/1.33 tff(1234,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1235,plain,
% 1.14/1.33 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1234, 1175, 28, 176, 1111, 1147])).
% 1.14/1.33 tff(1236,plain,
% 1.14/1.33 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1235, 1104])).
% 1.14/1.33 tff(1237,plain,
% 1.14/1.33 (r(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[743, 1236, 1098])).
% 1.14/1.33 tff(1238,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1239,plain,
% 1.14/1.33 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1240,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1239])).
% 1.14/1.33 tff(1241,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1240, 1238])).
% 1.14/1.33 tff(1242,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1243,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 1.14/1.33 tff(1244,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1243, 77, 794, 752, 360])).
% 1.14/1.33 tff(1245,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1246,plain,
% 1.14/1.33 (~r(s(s(elem!1)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1245, 1237, 360])).
% 1.14/1.33 tff(1247,plain,
% 1.14/1.33 (b(s(s(elem!1)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[808, 1246])).
% 1.14/1.33 tff(1248,plain,
% 1.14/1.33 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1247, 1074])).
% 1.14/1.33 tff(1249,plain,
% 1.14/1.33 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1069])).
% 1.14/1.33 tff(1250,plain,
% 1.14/1.33 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1072])).
% 1.14/1.33 tff(1251,plain,
% 1.14/1.33 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.14/1.33 inference(symmetry,[status(thm)],[1250])).
% 1.14/1.33 tff(1252,plain,
% 1.14/1.33 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1251])).
% 1.14/1.33 tff(1253,plain,
% 1.14/1.33 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1098, 1252])).
% 1.14/1.33 tff(1254,plain,
% 1.14/1.33 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1102])).
% 1.14/1.33 tff(1255,plain,
% 1.14/1.33 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1235, 1254])).
% 1.14/1.33 tff(1256,plain,
% 1.14/1.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(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(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1257,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1258,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 1.14/1.33 tff(1259,plain,
% 1.14/1.33 ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1258, 21])).
% 1.14/1.33 tff(1260,plain,
% 1.14/1.33 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1259, 1255, 1253])).
% 1.14/1.33 tff(1261,plain,
% 1.14/1.33 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1260, 1249])).
% 1.14/1.33 tff(1262,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1263,plain,
% 1.14/1.33 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1264,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1263])).
% 1.14/1.33 tff(1265,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1264, 1262])).
% 1.14/1.33 tff(1266,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1267,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.14/1.33 tff(1268,plain,
% 1.14/1.33 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1267, 77, 328, 1261])).
% 1.14/1.33 tff(1269,assumption,(s(s(z)) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.14/1.33 tff(1270,plain,
% 1.14/1.33 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1269])).
% 1.14/1.33 tff(1271,plain,
% 1.14/1.33 (s(z) = s(s(s(s(s(z)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[44, 1270, 1076])).
% 1.14/1.33 tff(1272,plain,
% 1.14/1.33 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1271])).
% 1.14/1.33 tff(1273,plain,
% 1.14/1.33 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.14/1.33 inference(symmetry,[status(thm)],[1272])).
% 1.14/1.33 tff(1274,plain,
% 1.14/1.33 (s(s(s(s(z)))) = z),
% 1.14/1.33 inference(transitivity,[status(thm)],[554, 1273, 47])).
% 1.14/1.33 tff(1275,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[242, 1274])).
% 1.14/1.33 tff(1276,plain,(~(s(s(z)) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1277,plain,
% 1.14/1.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1278,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1279,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.14/1.33 tff(1280,plain,
% 1.14/1.33 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1279, 21, 1276, 1268])).
% 1.14/1.33 tff(1281,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1282,plain,
% 1.14/1.33 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1283,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1282])).
% 1.14/1.33 tff(1284,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.14/1.33 tff(1285,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1286,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.14/1.33 tff(1287,plain,
% 1.14/1.33 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1286, 116, 270, 1158, 1048])).
% 1.14/1.33 tff(1288,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1287, 1280, 1248])).
% 1.14/1.33 tff(1289,plain,((elem!1 = z) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | (~b(s(s(s(s(z)))), z)) | r(elem!1, s(s(s(s(z))))) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1290,plain,
% 1.14/1.33 (r(elem!1, z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1289, 438, 176, 292, 1048, 328, 439, 28, 1047, 1046, 447, 360, 1040, 270])).
% 1.14/1.33 tff(1291,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1292,plain,
% 1.14/1.33 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1293,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1292])).
% 1.14/1.33 tff(1294,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1293, 1291])).
% 1.14/1.33 tff(1295,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1296,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.14/1.34 tff(1297,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1296, 116, 1055, 270, 271, 667])).
% 1.14/1.34 tff(1298,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1299,plain,
% 1.14/1.34 (~b(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1298, 1045, 271, 270])).
% 1.14/1.34 tff(1300,plain,
% 1.14/1.34 (r(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[633, 1299, 1046])).
% 1.14/1.34 tff(1301,plain,
% 1.14/1.34 (~r(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[628, 575, 620])).
% 1.14/1.34 tff(1302,plain,
% 1.14/1.34 (b(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[210, 1301])).
% 1.14/1.34 tff(1303,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.14/1.34 tff(1304,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1305,plain,
% 1.14/1.34 (((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1306,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1305])).
% 1.14/1.34 tff(1307,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1306, 1304])).
% 1.14/1.34 tff(1308,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1309,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 1.14/1.34 tff(1310,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1309, 116, 1055, 270, 1303, 1054, 1048])).
% 1.14/1.34 tff(1311,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1312,plain,
% 1.14/1.34 (~b(s(s(z)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1311, 1302, 1055, 1054, 1048])).
% 1.14/1.34 tff(1313,plain,
% 1.14/1.34 (r(s(s(z)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[25, 1312])).
% 1.14/1.34 tff(1314,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1315,plain,
% 1.14/1.34 (((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1316,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1315])).
% 1.14/1.34 tff(1317,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1316, 1314])).
% 1.14/1.34 tff(1318,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1319,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.14/1.34 tff(1320,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1319, 77, 575, 1313, 428])).
% 1.14/1.34 tff(1321,plain,((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1322,plain,
% 1.14/1.34 (~b(elem!1, s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1321, 1300, 1048, 1290, 1045, 427])).
% 1.14/1.34 tff(1323,plain,
% 1.14/1.34 (elem!1 = s(s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1068, 1322, 438])).
% 1.14/1.34 tff(1324,plain,
% 1.14/1.34 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1323])).
% 1.14/1.34 tff(1325,plain,
% 1.14/1.34 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 1.14/1.34 inference(symmetry,[status(thm)],[1324])).
% 1.14/1.34 tff(1326,plain,
% 1.14/1.34 ((~r(s(s(s(s(z)))), z)) <=> (~r(elem!1, z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1325])).
% 1.14/1.34 tff(1327,plain,
% 1.14/1.34 (~r(elem!1, z)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[240, 1326])).
% 1.14/1.34 tff(1328,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1290, 1327])).
% 1.14/1.34 tff(1329,plain,(b(s(s(z)), elem!1) | r(s(s(s(s(z)))), z) | (~b(s(s(z)), s(z))) | (elem!1 = s(z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), elem!1)) | b(s(s(z)), z) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1330,plain,
% 1.14/1.34 (b(s(s(z)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1329, 421, 392, 345, 415, 270, 176, 352, 342, 410, 28, 403, 358, 2, 377])).
% 1.14/1.34 tff(1331,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.14/1.34 tff(1332,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.14/1.34 tff(1333,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))), s(s(z)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1334,plain,
% 1.14/1.34 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~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))), s(s(z)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1335,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))), s(s(z))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1334])).
% 1.14/1.34 tff(1336,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))), s(s(z)))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1335, 1333])).
% 1.14/1.34 tff(1337,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1338,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.14/1.34 tff(1339,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1338, 116, 1332, 27, 1331, 176])).
% 1.14/1.34 tff(1340,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1341,plain,
% 1.14/1.34 (~b(elem!1, s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1340, 1330, 176, 27])).
% 1.14/1.34 tff(1342,plain,
% 1.14/1.34 (((~![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)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1343,plain,
% 1.14/1.34 ((~![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)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1344,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.14/1.34 tff(1345,plain,
% 1.14/1.34 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1344, 21])).
% 1.14/1.34 tff(1346,plain,
% 1.14/1.34 (elem!1 = s(s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1345, 1341, 369])).
% 1.14/1.34 tff(1347,plain,
% 1.14/1.34 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1346])).
% 1.14/1.34 tff(1348,plain,
% 1.14/1.34 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 1.14/1.34 inference(symmetry,[status(thm)],[1347])).
% 1.14/1.34 tff(1349,plain,
% 1.14/1.34 ((~b(z, s(s(s(z))))) <=> (~b(z, elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1348])).
% 1.14/1.34 tff(1350,plain,
% 1.14/1.34 (~b(z, elem!1)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[411, 1349])).
% 1.14/1.34 tff(1351,plain,
% 1.14/1.34 (~(z = elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[445, 410])).
% 1.14/1.34 tff(1352,plain,
% 1.14/1.34 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1077])).
% 1.14/1.34 tff(1353,plain,
% 1.14/1.34 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[1352])).
% 1.14/1.34 tff(1354,plain,
% 1.14/1.34 (b(elem!1, s(s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[28, 1353])).
% 1.14/1.34 tff(1355,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.14/1.34 tff(1356,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1355, 1354])).
% 1.14/1.34 tff(1357,plain,((~(elem!1 = s(s(s(s(z)))))) | b(elem!1, s(s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1358,plain,
% 1.14/1.34 (~(elem!1 = s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1357, 1341, 28])).
% 1.14/1.34 tff(1359,plain,
% 1.14/1.34 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[832])).
% 1.14/1.34 tff(1360,plain,
% 1.14/1.34 (elem!1 = inj_0(s(elem!1))),
% 1.14/1.34 inference(symmetry,[status(thm)],[460])).
% 1.14/1.34 tff(1361,plain,
% 1.14/1.34 (elem!1 = s(s(s(s(z))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1360, 1359, 553])).
% 1.14/1.34 tff(1362,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.34 tff(1363,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1362, 1361])).
% 1.14/1.34 tff(1364,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1365,plain,
% 1.14/1.34 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1364, 1358])).
% 1.14/1.34 tff(1366,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.14/1.34 tff(1367,plain,
% 1.14/1.34 (s(elem!1) = s(s(s(s(z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1366])).
% 1.14/1.34 tff(1368,plain,
% 1.14/1.34 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1367])).
% 1.14/1.34 tff(1369,plain,
% 1.14/1.34 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1368])).
% 1.14/1.34 tff(1370,plain,
% 1.14/1.34 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1369])).
% 1.14/1.34 tff(1371,plain,
% 1.14/1.34 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1366])).
% 1.14/1.34 tff(1372,plain,
% 1.14/1.34 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1371])).
% 1.14/1.34 tff(1373,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.14/1.34 tff(1374,plain,
% 1.14/1.34 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.14/1.34 tff(1375,plain,
% 1.14/1.34 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1374, 1370])).
% 1.14/1.34 tff(1376,plain,
% 1.14/1.34 (((~![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)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1377,plain,
% 1.14/1.34 ((~![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)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1378,plain,
% 1.14/1.34 ((~![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))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 1.14/1.34 tff(1379,plain,
% 1.14/1.34 ((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))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1378, 21])).
% 1.14/1.34 tff(1380,plain,
% 1.14/1.34 (b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1379, 1138])).
% 1.14/1.34 tff(1381,plain,
% 1.14/1.34 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1380, 1375])).
% 1.14/1.34 tff(1382,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1383,plain,
% 1.14/1.34 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1384,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1383])).
% 1.14/1.34 tff(1385,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1384, 1382])).
% 1.14/1.34 tff(1386,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1387,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.14/1.34 tff(1388,plain,
% 1.14/1.34 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1387, 116, 27, 176, 1381])).
% 1.14/1.34 tff(1389,plain,
% 1.14/1.34 (((~![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))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1390,plain,
% 1.14/1.34 ((~![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))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1391,plain,
% 1.14/1.34 ((~![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)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 1.14/1.34 tff(1392,plain,
% 1.14/1.34 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 1388])).
% 1.14/1.34 tff(1393,plain,
% 1.14/1.34 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(1394,plain,
% 1.14/1.34 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1367])).
% 1.14/1.34 tff(1395,plain,
% 1.14/1.34 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1394, 1393])).
% 1.14/1.34 tff(1396,plain,
% 1.14/1.34 ((~(s(elem!1) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1395])).
% 1.14/1.34 tff(1397,plain,
% 1.14/1.34 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[855, 1396])).
% 1.14/1.34 tff(1398,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1399,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1400,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 1.14/1.34 tff(1401,plain,
% 1.14/1.34 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1400, 116, 27, 28, 176, 1381])).
% 1.14/1.34 tff(1402,plain,
% 1.14/1.34 (((~![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))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1403,plain,
% 1.14/1.34 ((~![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))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1404,plain,
% 1.14/1.34 ((~![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)))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.14/1.34 tff(1405,plain,
% 1.14/1.34 ((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)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1404, 21])).
% 1.14/1.34 tff(1406,plain,
% 1.14/1.34 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1405, 1401, 1397])).
% 1.14/1.34 tff(1407,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1408,plain,
% 1.14/1.34 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1409,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1408])).
% 1.14/1.34 tff(1410,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1409, 1407])).
% 1.14/1.34 tff(1411,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1412,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.14/1.34 tff(1413,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1412, 77, 66, 342, 1406, 1392])).
% 1.14/1.34 tff(1414,plain,((~(elem!1 = s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (s(elem!1) = s(s(s(s(s(z)))))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1415,plain,
% 1.14/1.34 (r(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1414, 1365, 27, 28, 176, 26, 1346])).
% 1.14/1.34 tff(1416,plain,
% 1.14/1.34 (~r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1245, 752, 360])).
% 1.14/1.34 tff(1417,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1418,plain,
% 1.14/1.34 (((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1419,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1418])).
% 1.14/1.34 tff(1420,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1419, 1417])).
% 1.14/1.34 tff(1421,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1422,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.14/1.34 tff(1423,plain,
% 1.14/1.34 (~r(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1422, 77, 448, 752])).
% 1.14/1.34 tff(1424,plain,
% 1.14/1.34 (((~![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))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1425,plain,
% 1.14/1.34 ((~![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))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1426,plain,
% 1.14/1.35 ((~![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)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 1.14/1.35 tff(1427,plain,
% 1.14/1.35 (b(s(s(elem!1)), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1426, 21, 508, 1423])).
% 1.14/1.35 tff(1428,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1429,plain,
% 1.14/1.35 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1430,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1429])).
% 1.14/1.35 tff(1431,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1430, 1428])).
% 1.14/1.35 tff(1432,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1433,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 1.14/1.35 tff(1434,plain,
% 1.14/1.35 (~r(z, s(s(elem!1)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1433, 77, 448, 752])).
% 1.14/1.35 tff(1435,plain,
% 1.14/1.35 (b(z, s(s(elem!1)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[514, 1434])).
% 1.14/1.35 tff(1436,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.14/1.35 tff(1437,plain,
% 1.14/1.35 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1438,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1437])).
% 1.14/1.35 tff(1439,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1438, 971])).
% 1.14/1.35 tff(1440,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1441,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 1.14/1.35 tff(1442,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1441, 116, 1436, 270, 1435, 1427])).
% 1.14/1.35 tff(1443,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1444,plain,
% 1.14/1.35 (~b(s(s(elem!1)), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1443, 752, 448, 270])).
% 1.14/1.35 tff(1445,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[808, 1444, 1416])).
% 1.14/1.35 tff(1446,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1447,plain,
% 1.14/1.35 (~r(z, elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1446, 1415, 270, 358])).
% 1.14/1.35 tff(1448,plain,
% 1.14/1.35 (b(z, elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1044, 1447, 1351])).
% 1.14/1.35 tff(1449,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1448, 1350])).
% 1.14/1.35 tff(1450,plain,((s(z) = elem!1) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(z)), z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1451,plain,
% 1.14/1.35 (s(z) = elem!1),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1450, 340, 106, 28, 90, 2, 211])).
% 1.14/1.35 tff(1452,plain,
% 1.14/1.35 (b(s(z), z) <=> b(elem!1, z)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[466])).
% 1.14/1.35 tff(1453,plain,
% 1.14/1.35 (b(elem!1, z) <=> b(s(z), z)),
% 1.14/1.35 inference(symmetry,[status(thm)],[1452])).
% 1.14/1.35 tff(1454,plain,
% 1.14/1.35 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1453])).
% 1.14/1.35 tff(1455,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.14/1.35 tff(1456,plain,
% 1.14/1.35 (~b(s(z), z)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 1.14/1.35 tff(1457,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[270, 1456])).
% 1.14/1.35 tff(1458,plain,((~(s(z) = elem!1)) | (~b(s(z), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1459,plain,
% 1.14/1.35 (b(elem!1, z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1458, 1451, 211])).
% 1.14/1.35 tff(1460,plain,
% 1.14/1.35 (~(s(s(z)) = elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[376, 340, 338])).
% 1.14/1.35 tff(1461,plain,
% 1.14/1.35 (~r(s(s(z)), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[383, 77, 150, 326])).
% 1.14/1.35 tff(1462,plain,
% 1.14/1.35 (b(s(s(z)), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[391, 21, 388, 1461])).
% 1.14/1.35 tff(1463,plain,
% 1.14/1.35 (~b(s(s(s(z))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[398, 116, 211, 90, 1462, 338])).
% 1.14/1.35 tff(1464,plain,
% 1.14/1.35 (r(s(s(s(z))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[402, 21, 135, 1463])).
% 1.14/1.35 tff(1465,plain,
% 1.14/1.35 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1366])).
% 1.14/1.35 tff(1466,plain,
% 1.14/1.35 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 1.14/1.35 inference(symmetry,[status(thm)],[1465])).
% 1.14/1.35 tff(1467,plain,
% 1.14/1.35 ((~b(s(s(s(z))), z)) <=> (~b(elem!1, z))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1466])).
% 1.14/1.35 tff(1468,plain,
% 1.14/1.35 (~b(elem!1, z)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[57, 1467])).
% 1.14/1.35 tff(1469,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[537, 1468])).
% 1.14/1.35 tff(1470,plain,((~(elem!1 = s(s(s(z))))) | (~b(elem!1, z)) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1471,plain,
% 1.14/1.35 (~(elem!1 = s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1470, 1459, 57])).
% 1.14/1.35 tff(1472,plain,
% 1.14/1.35 (~(elem!1 = z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[409, 340, 211])).
% 1.14/1.35 tff(1473,plain,
% 1.14/1.35 (~(z = elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[445, 1472])).
% 1.14/1.35 tff(1474,plain,
% 1.14/1.35 (s(s(z)) = s(elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[466])).
% 1.14/1.35 tff(1475,plain,
% 1.14/1.35 (s(s(s(z))) = s(s(elem!1))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1474])).
% 1.14/1.35 tff(1476,plain,
% 1.14/1.35 (s(s(elem!1)) = s(s(s(z)))),
% 1.14/1.35 inference(symmetry,[status(thm)],[1475])).
% 1.14/1.35 tff(1477,plain,
% 1.14/1.35 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1476])).
% 1.14/1.35 tff(1478,plain,
% 1.14/1.35 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 1.14/1.35 inference(symmetry,[status(thm)],[1477])).
% 1.14/1.35 tff(1479,plain,
% 1.14/1.35 (r(s(s(elem!1)), z)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[67, 1478])).
% 1.14/1.35 tff(1480,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 1.14/1.35 tff(1481,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1480, 1479])).
% 1.14/1.35 tff(1482,plain,(r(s(s(elem!1)), z) | (~r(s(s(s(z))), z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1483,plain,
% 1.14/1.35 (r(s(s(elem!1)), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1482, 466, 67])).
% 1.14/1.35 tff(1484,plain,
% 1.14/1.35 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1475])).
% 1.14/1.35 tff(1485,plain,
% 1.14/1.35 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[466])).
% 1.14/1.35 tff(1486,plain,
% 1.14/1.35 (r(s(s(s(z))), elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1047, 1485])).
% 1.14/1.35 tff(1487,plain,
% 1.14/1.35 (r(s(s(elem!1)), elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1486, 1484])).
% 1.14/1.35 tff(1488,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1422, 77, 448, 1487, 1483])).
% 1.14/1.35 tff(1489,plain,((~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1490,plain,
% 1.14/1.35 (~r(z, elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1489, 1451, 64, 1464])).
% 1.14/1.35 tff(1491,plain,
% 1.14/1.35 (b(z, elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1044, 1490, 1473])).
% 1.14/1.35 tff(1492,plain,
% 1.14/1.35 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[466])).
% 1.14/1.35 tff(1493,plain,
% 1.14/1.35 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1492])).
% 1.14/1.35 tff(1494,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 1.14/1.35 tff(1495,plain,
% 1.14/1.35 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1494])).
% 1.14/1.35 tff(1496,plain,
% 1.14/1.35 (s(s(s(s(s(z))))) = z),
% 1.14/1.35 inference(transitivity,[status(thm)],[1195, 1495, 47])).
% 1.14/1.35 tff(1497,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[895, 1496])).
% 1.14/1.35 tff(1498,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1499,plain,
% 1.14/1.35 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1498, 1493])).
% 1.14/1.35 tff(1500,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.35 tff(1501,plain,
% 1.14/1.35 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1500])).
% 1.14/1.35 tff(1502,plain,
% 1.14/1.35 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[1501])).
% 1.14/1.35 tff(1503,plain,
% 1.14/1.35 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1476, 128, 1502, 1076])).
% 1.14/1.35 tff(1504,plain,
% 1.14/1.35 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(1505,plain,
% 1.14/1.35 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1475])).
% 1.14/1.35 tff(1506,plain,
% 1.14/1.35 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1505, 1504])).
% 1.14/1.35 tff(1507,plain,
% 1.14/1.35 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1506])).
% 1.14/1.35 tff(1508,plain,
% 1.14/1.35 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1138, 1507])).
% 1.14/1.35 tff(1509,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1508, 1503])).
% 1.14/1.35 tff(1510,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1511,plain,
% 1.14/1.35 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1510, 466])).
% 1.14/1.35 tff(1512,plain,
% 1.14/1.35 (s(elem!1) = s(s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[1474])).
% 1.14/1.35 tff(1513,plain,
% 1.14/1.35 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1512])).
% 1.14/1.35 tff(1514,plain,
% 1.14/1.35 ((~b(z, s(elem!1))) <=> (~b(z, s(s(z))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1513])).
% 1.14/1.35 tff(1515,plain,
% 1.14/1.35 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[220, 28, 27, 176])).
% 1.14/1.35 tff(1516,plain,
% 1.14/1.35 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[226, 1515])).
% 1.14/1.35 tff(1517,plain,
% 1.14/1.35 (~r(s(s(s(s(z)))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[237, 1516, 66])).
% 1.14/1.35 tff(1518,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[247, 1517])).
% 1.14/1.35 tff(1519,plain,
% 1.14/1.35 (~b(elem!1, s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1063, 1055, 1518, 537])).
% 1.14/1.35 tff(1520,plain,
% 1.14/1.35 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1512])).
% 1.14/1.35 tff(1521,plain,
% 1.14/1.35 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[1520])).
% 1.14/1.35 tff(1522,plain,
% 1.14/1.35 (r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[328, 1521])).
% 1.14/1.35 tff(1523,plain,
% 1.14/1.35 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1474])).
% 1.14/1.35 tff(1524,plain,
% 1.14/1.35 (r(s(elem!1), elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[428, 1523])).
% 1.14/1.35 tff(1525,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.35 tff(1526,plain,
% 1.14/1.35 (s(z) = s(s(s(s(z))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[466, 1077])).
% 1.14/1.35 tff(1527,plain,
% 1.14/1.35 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1526])).
% 1.14/1.35 tff(1528,plain,
% 1.14/1.35 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[1527])).
% 1.14/1.35 tff(1529,plain,
% 1.14/1.35 (s(s(elem!1)) = z),
% 1.14/1.35 inference(transitivity,[status(thm)],[1476, 128, 1528, 47])).
% 1.14/1.35 tff(1530,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[508, 1529])).
% 1.14/1.35 tff(1531,plain,((~(elem!1 = s(s(s(s(z)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1532,plain,
% 1.14/1.35 (~(elem!1 = s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1531, 466])).
% 1.14/1.35 tff(1533,plain,
% 1.14/1.35 (r(elem!1, s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1068, 1532, 1525])).
% 1.14/1.35 tff(1534,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1535,plain,
% 1.14/1.35 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1536,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1535])).
% 1.14/1.35 tff(1537,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1536, 1534])).
% 1.14/1.35 tff(1538,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1539,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 1.14/1.35 tff(1540,plain,
% 1.14/1.35 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1539, 77, 1533, 1524])).
% 1.14/1.35 tff(1541,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1540, 1522])).
% 1.14/1.35 tff(1542,plain,((~(s(z) = elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1543,plain,
% 1.14/1.35 (~r(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1542, 466, 342, 1519])).
% 1.14/1.35 tff(1544,plain,
% 1.14/1.35 (b(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[426, 1543, 422])).
% 1.14/1.35 tff(1545,plain,
% 1.14/1.35 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1512])).
% 1.14/1.35 tff(1546,plain,
% 1.14/1.35 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.14/1.35 inference(symmetry,[status(thm)],[1545])).
% 1.14/1.35 tff(1547,plain,
% 1.14/1.35 (b(s(elem!1), elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1331, 1546])).
% 1.14/1.35 tff(1548,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[779, 1547])).
% 1.14/1.35 tff(1549,plain,(b(s(elem!1), elem!1) | (~b(s(s(z)), elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1550,plain,
% 1.14/1.35 (b(s(elem!1), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1549, 1544, 466])).
% 1.14/1.35 tff(1551,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1552,plain,
% 1.14/1.35 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1553,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1552])).
% 1.14/1.35 tff(1554,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1553, 1551])).
% 1.14/1.35 tff(1555,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1556,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 1.14/1.35 tff(1557,plain,
% 1.14/1.35 (~b(z, s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1556, 116, 1055, 537, 1550])).
% 1.14/1.35 tff(1558,plain,
% 1.14/1.35 (~b(z, s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1557, 1514])).
% 1.14/1.35 tff(1559,plain,
% 1.14/1.35 (r(z, s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1174, 1558])).
% 1.14/1.35 tff(1560,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.35 tff(1561,plain,
% 1.14/1.35 (s(s(s(s(z)))) = z),
% 1.14/1.35 inference(symmetry,[status(thm)],[1560])).
% 1.14/1.35 tff(1562,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[242, 1561])).
% 1.14/1.35 tff(1563,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1564,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.35 tff(1565,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1566,plain,
% 1.14/1.35 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1567,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1566])).
% 1.14/1.35 tff(1568,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1567, 1565])).
% 1.14/1.35 tff(1569,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1570,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 1.14/1.35 tff(1571,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1570, 77, 229, 1212, 1564])).
% 1.14/1.35 tff(1572,plain,((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1573,plain,
% 1.14/1.35 (~r(z, s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1572, 1559, 1516])).
% 1.14/1.35 tff(1574,plain,
% 1.14/1.35 (((~![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))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1575,plain,
% 1.14/1.35 ((~![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))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1576,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 1.14/1.35 tff(1577,plain,
% 1.14/1.35 (b(z, s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1576, 21, 1573, 1563])).
% 1.14/1.35 tff(1578,plain,
% 1.14/1.35 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1476])).
% 1.14/1.35 tff(1579,plain,
% 1.14/1.35 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1578])).
% 1.14/1.35 tff(1580,plain,
% 1.14/1.35 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(1581,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.14/1.35 tff(1582,plain,
% 1.14/1.35 (elem!1 = s(s(s(s(z))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.14/1.35 tff(1583,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1362, 1582])).
% 1.14/1.35 tff(1584,plain,((~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(1585,plain,
% 1.14/1.35 (~(s(s(s(s(z)))) = elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1584, 1532])).
% 1.14/1.35 tff(1586,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1587,plain,
% 1.14/1.35 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1588,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1587])).
% 1.14/1.35 tff(1589,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1588, 1586])).
% 1.14/1.35 tff(1590,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1591,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 1.14/1.35 tff(1592,plain,
% 1.14/1.35 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1591, 116, 1055, 537, 1518])).
% 1.14/1.35 tff(1593,plain,
% 1.14/1.35 (((~![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))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1594,plain,
% 1.14/1.35 ((~![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))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1595,plain,
% 1.14/1.36 ((~![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)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 1.14/1.36 tff(1596,plain,
% 1.14/1.36 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1595, 21])).
% 1.14/1.36 tff(1597,plain,
% 1.14/1.36 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1596, 1592, 1585])).
% 1.14/1.36 tff(1598,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1599,plain,
% 1.14/1.36 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1600,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1599])).
% 1.14/1.36 tff(1601,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1600, 1598])).
% 1.14/1.36 tff(1602,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1603,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.14/1.36 tff(1604,plain,
% 1.14/1.36 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1603, 77, 1487, 1597])).
% 1.14/1.36 tff(1605,plain,
% 1.14/1.36 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1604, 1579])).
% 1.14/1.36 tff(1606,plain,
% 1.14/1.36 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1146, 1605])).
% 1.14/1.36 tff(1607,plain,
% 1.14/1.36 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1234, 1606, 28, 176, 1577, 1559])).
% 1.14/1.36 tff(1608,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.36 tff(1609,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.36 tff(1610,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.36 tff(1611,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1612,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1613,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 1.14/1.36 tff(1614,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1613, 21, 1610, 1609, 1608])).
% 1.14/1.36 tff(1615,plain,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1616,plain,
% 1.14/1.36 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1615, 1607, 1511])).
% 1.14/1.36 tff(1617,plain,
% 1.14/1.36 (r(elem!1, s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1068, 1532, 1519])).
% 1.14/1.36 tff(1618,plain,
% 1.14/1.36 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1476])).
% 1.14/1.36 tff(1619,plain,
% 1.14/1.36 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[1618])).
% 1.14/1.36 tff(1620,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.14/1.36 tff(1621,plain,
% 1.14/1.36 (~b(elem!1, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1340, 1544, 27, 176])).
% 1.14/1.36 tff(1622,plain,
% 1.14/1.36 (r(elem!1, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1345, 1621, 1620])).
% 1.14/1.36 tff(1623,plain,
% 1.14/1.36 (r(elem!1, s(s(elem!1)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1622, 1619])).
% 1.14/1.36 tff(1624,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1625,plain,
% 1.14/1.36 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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)))))), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1626,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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)))))), elem!1))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1625])).
% 1.14/1.36 tff(1627,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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)))))), elem!1)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1626, 1624])).
% 1.14/1.36 tff(1628,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1629,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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)))))), elem!1))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.14/1.36 tff(1630,plain,
% 1.14/1.36 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1629, 77, 1623, 1617, 1616])).
% 1.14/1.36 tff(1631,plain,
% 1.14/1.36 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1259, 1630, 1499])).
% 1.14/1.36 tff(1632,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1633,plain,
% 1.14/1.36 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1634,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1633])).
% 1.14/1.36 tff(1635,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1634, 1632])).
% 1.14/1.36 tff(1636,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1637,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 1.14/1.36 tff(1638,plain,
% 1.14/1.36 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1637, 116, 1055, 537, 1550, 1631])).
% 1.14/1.36 tff(1639,plain,
% 1.14/1.36 (r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[342, 1521])).
% 1.14/1.36 tff(1640,plain,
% 1.14/1.36 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1474])).
% 1.14/1.36 tff(1641,plain,
% 1.14/1.36 (r(s(elem!1), z)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[66, 1640])).
% 1.14/1.36 tff(1642,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1643,plain,
% 1.14/1.36 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1644,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1643])).
% 1.14/1.36 tff(1645,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1644, 1642])).
% 1.14/1.36 tff(1646,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1647,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.14/1.36 tff(1648,plain,
% 1.14/1.36 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1647, 77, 1641, 1616, 1639])).
% 1.14/1.36 tff(1649,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1650,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1651,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.14/1.36 tff(1652,plain,
% 1.14/1.36 ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1651, 21, 1648])).
% 1.14/1.36 tff(1653,plain,
% 1.14/1.36 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1652, 1638])).
% 1.14/1.36 tff(1654,plain,
% 1.14/1.36 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[1653])).
% 1.14/1.36 tff(1655,plain,
% 1.14/1.36 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1474, 1654])).
% 1.14/1.36 tff(1656,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1276, 1655])).
% 1.14/1.36 tff(1657,plain,((~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1658,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1657, 1491, 1471, 1464, 28, 90, 26, 1460, 1451, 106, 1459])).
% 1.14/1.36 tff(1659,plain,(b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1660,plain,
% 1.14/1.36 (b(s(z), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1659, 57, 28, 2])).
% 1.14/1.36 tff(1661,plain,
% 1.14/1.36 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1366])).
% 1.14/1.36 tff(1662,plain,
% 1.14/1.36 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.14/1.36 inference(symmetry,[status(thm)],[1661])).
% 1.14/1.36 tff(1663,plain,
% 1.14/1.36 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1662])).
% 1.14/1.36 tff(1664,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.14/1.36 tff(1665,plain,
% 1.14/1.36 (~b(s(z), elem!1)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.14/1.36 tff(1666,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[847, 1665])).
% 1.14/1.36 tff(1667,plain,((~(elem!1 = s(s(s(z))))) | (~b(s(z), elem!1)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1668,plain,
% 1.14/1.36 (~(elem!1 = s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1667, 1660, 339])).
% 1.14/1.36 tff(1669,plain,
% 1.14/1.36 (r(s(z), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[194, 339])).
% 1.14/1.36 tff(1670,plain,
% 1.14/1.36 (~b(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[263, 106, 28, 248, 90])).
% 1.14/1.36 tff(1671,plain,
% 1.14/1.36 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[267, 21, 1670])).
% 1.14/1.36 tff(1672,plain,
% 1.14/1.36 (r(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1671, 253])).
% 1.14/1.36 tff(1673,plain,
% 1.14/1.36 (~r(s(s(z)), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[456, 448, 26])).
% 1.14/1.36 tff(1674,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(1675,plain,
% 1.14/1.36 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[404])).
% 1.14/1.36 tff(1676,plain,
% 1.14/1.36 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.14/1.36 inference(symmetry,[status(thm)],[1675])).
% 1.14/1.36 tff(1677,plain,
% 1.14/1.36 ((~b(s(s(z)), z)) <=> (~b(s(s(z)), elem!1))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1676])).
% 1.14/1.36 tff(1678,plain,
% 1.14/1.36 (~b(s(s(z)), elem!1)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2, 1677])).
% 1.14/1.36 tff(1679,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1331, 1678])).
% 1.14/1.36 tff(1680,plain,((~(elem!1 = z)) | (~b(s(s(z)), elem!1)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1681,plain,
% 1.14/1.36 (~b(s(s(z)), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1680, 404, 2])).
% 1.14/1.36 tff(1682,plain,
% 1.14/1.36 (s(s(z)) = elem!1),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[426, 1681, 1674])).
% 1.14/1.36 tff(1683,plain,
% 1.14/1.36 (s(s(z)) = z),
% 1.14/1.36 inference(transitivity,[status(thm)],[1682, 404])).
% 1.14/1.36 tff(1684,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[11, 1683])).
% 1.14/1.36 tff(1685,plain,((~(elem!1 = z)) | r(s(s(z)), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1686,plain,
% 1.14/1.36 (~(elem!1 = z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1685, 1673, 2])).
% 1.14/1.36 tff(1687,plain,
% 1.14/1.36 (~(z = elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[445, 1686])).
% 1.14/1.36 tff(1688,plain,
% 1.14/1.36 (b(s(s(z)), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1039, 1687, 2, 254, 328, 448])).
% 1.14/1.36 tff(1689,plain,
% 1.14/1.36 (~b(elem!1, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1340, 1688, 176, 27])).
% 1.14/1.36 tff(1690,plain,
% 1.14/1.36 (r(elem!1, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1345, 1689, 1620])).
% 1.14/1.36 tff(1691,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1692,plain,
% 1.14/1.36 (((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(1693,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1692])).
% 1.14/1.36 tff(1694,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1693, 1691])).
% 1.14/1.36 tff(1695,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(1696,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 1.14/1.36 tff(1697,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1696, 77, 448, 1690, 291])).
% 1.14/1.36 tff(1698,plain,((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | b(s(s(z)), z) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1699,plain,
% 1.14/1.36 (~r(z, elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1698, 1672, 1668, 90, 106, 2, 248, 150])).
% 1.14/1.36 tff(1700,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(1701,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.36 tff(1702,plain,
% 1.14/1.36 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1701])).
% 1.14/1.36 tff(1703,plain,
% 1.14/1.36 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[1702])).
% 1.14/1.36 tff(1704,plain,
% 1.14/1.36 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[554, 1703, 127])).
% 1.14/1.36 tff(1705,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 1.14/1.36 tff(1706,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1705, 1704])).
% 1.14/1.36 tff(1707,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(1708,plain,
% 1.14/1.36 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1707, 1140])).
% 1.14/1.36 tff(1709,plain,
% 1.14/1.36 (s(z) = s(elem!1)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.36 tff(1710,plain,
% 1.14/1.36 (s(elem!1) = s(z)),
% 1.14/1.36 inference(symmetry,[status(thm)],[1709])).
% 1.14/1.36 tff(1711,plain,
% 1.14/1.36 (r(s(elem!1), s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1710])).
% 1.14/1.36 tff(1712,plain,
% 1.14/1.36 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[1711])).
% 1.14/1.36 tff(1713,plain,
% 1.14/1.36 (elem!1 = z),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[445, 442])).
% 1.14/1.36 tff(1714,plain,
% 1.14/1.36 (r(s(s(z)), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1685, 1713, 2])).
% 1.14/1.36 tff(1715,plain,
% 1.14/1.36 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.36 tff(1716,plain,
% 1.14/1.36 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1715, 1580])).
% 1.14/1.36 tff(1717,plain,
% 1.14/1.36 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1716])).
% 1.14/1.36 tff(1718,plain,
% 1.14/1.36 (~(elem!1 = s(s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[242, 1717])).
% 1.14/1.36 tff(1719,plain,
% 1.14/1.36 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.14/1.36 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.36 tff(1720,plain,
% 1.14/1.36 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[346, 1719])).
% 1.14/1.36 tff(1721,plain,
% 1.14/1.37 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.37 tff(1722,plain,
% 1.14/1.37 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1721])).
% 1.14/1.37 tff(1723,plain,
% 1.14/1.37 (~(s(z) = elem!1)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[206, 1722])).
% 1.14/1.37 tff(1724,plain,
% 1.14/1.37 (b(s(z), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[357, 1723, 1700])).
% 1.14/1.37 tff(1725,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.14/1.37 tff(1726,plain,
% 1.14/1.37 (~r(elem!1, s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[437, 328, 428])).
% 1.14/1.37 tff(1727,plain,
% 1.14/1.37 (b(elem!1, s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1068, 1726, 1362])).
% 1.14/1.37 tff(1728,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1729,plain,
% 1.14/1.37 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1730,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1729])).
% 1.14/1.37 tff(1731,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[1730, 1728])).
% 1.14/1.37 tff(1732,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1733,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 1.14/1.37 tff(1734,plain,
% 1.14/1.37 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1733, 116, 847, 1727, 28, 1725])).
% 1.14/1.37 tff(1735,plain,
% 1.14/1.37 (~r(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[336, 328, 156])).
% 1.14/1.37 tff(1736,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[323, 21, 320, 1735, 1734])).
% 1.14/1.37 tff(1737,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(1738,plain,
% 1.14/1.37 (~r(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1737, 1724, 28, 1720, 1718, 342, 1714])).
% 1.14/1.37 tff(1739,plain,
% 1.14/1.37 (b(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[172, 1738])).
% 1.14/1.37 tff(1740,plain,
% 1.14/1.37 (~b(s(z), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[184, 1739, 176, 27])).
% 1.14/1.37 tff(1741,plain,
% 1.14/1.37 (r(s(z), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[194, 1740])).
% 1.14/1.37 tff(1742,plain,
% 1.14/1.37 (r(s(elem!1), s(s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1741, 1712])).
% 1.14/1.37 tff(1743,plain,
% 1.14/1.37 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[591])).
% 1.14/1.37 tff(1744,plain,
% 1.14/1.37 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1743])).
% 1.14/1.37 tff(1745,plain,
% 1.14/1.37 (elem!1 = z),
% 1.14/1.37 inference(symmetry,[status(thm)],[442])).
% 1.14/1.37 tff(1746,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.14/1.37 tff(1747,plain,
% 1.14/1.37 (s(s(s(z))) = z),
% 1.14/1.37 inference(transitivity,[status(thm)],[1746, 1745])).
% 1.14/1.37 tff(1748,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[59, 1747])).
% 1.14/1.37 tff(1749,plain,((~(s(s(s(z))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(1750,plain,
% 1.14/1.37 (~(s(s(s(z))) = elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1749, 442])).
% 1.14/1.37 tff(1751,plain,
% 1.14/1.37 (~(elem!1 = s(s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1750, 1744])).
% 1.14/1.37 tff(1752,plain,
% 1.14/1.37 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.14/1.37 inference(commutativity,[status(thm)],[])).
% 1.14/1.37 tff(1753,plain,
% 1.14/1.37 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1710])).
% 1.14/1.37 tff(1754,plain,
% 1.14/1.37 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[1753, 1752])).
% 1.14/1.37 tff(1755,plain,
% 1.14/1.37 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.14/1.37 inference(symmetry,[status(thm)],[1754])).
% 1.14/1.37 tff(1756,plain,
% 1.14/1.37 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1755])).
% 1.14/1.37 tff(1757,plain,
% 1.14/1.37 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[320, 1756])).
% 1.14/1.37 tff(1758,plain,
% 1.14/1.37 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.37 tff(1759,plain,
% 1.14/1.37 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1758])).
% 1.14/1.37 tff(1760,plain,
% 1.14/1.37 (~(s(elem!1) = elem!1)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[564, 1759])).
% 1.14/1.37 tff(1761,plain,
% 1.14/1.37 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1709])).
% 1.14/1.37 tff(1762,plain,
% 1.14/1.37 ((~r(s(z), elem!1)) <=> (~r(s(elem!1), elem!1))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1761])).
% 1.14/1.37 tff(1763,plain,
% 1.14/1.37 (~r(s(elem!1), elem!1)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1700, 1762])).
% 1.14/1.37 tff(1764,plain,
% 1.14/1.37 (b(s(elem!1), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[781, 1763, 1760])).
% 1.14/1.37 tff(1765,plain,
% 1.14/1.37 (~r(elem!1, s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[437, 1714, 342])).
% 1.14/1.37 tff(1766,plain,
% 1.14/1.37 (b(elem!1, s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1068, 1718, 1765])).
% 1.14/1.37 tff(1767,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1768,plain,
% 1.14/1.37 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1769,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1768])).
% 1.14/1.37 tff(1770,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[1769, 1767])).
% 1.14/1.37 tff(1771,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1772,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 1.14/1.37 tff(1773,plain,
% 1.14/1.37 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1772, 116, 1766, 28, 1764, 1720])).
% 1.14/1.37 tff(1774,plain,
% 1.14/1.37 (((~![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)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1775,plain,
% 1.14/1.37 ((~![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)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1776,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.14/1.37 tff(1777,plain,
% 1.14/1.37 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1776, 21, 1773])).
% 1.14/1.37 tff(1778,plain,
% 1.14/1.37 (r(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1777, 1757])).
% 1.14/1.37 tff(1779,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.14/1.37 tff(1780,plain,
% 1.14/1.37 (s(s(s(z))) = s(z)),
% 1.14/1.37 inference(transitivity,[status(thm)],[1779, 1710])).
% 1.14/1.37 tff(1781,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[135, 1780])).
% 1.14/1.37 tff(1782,plain,((~(s(s(s(z))) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(1783,plain,
% 1.14/1.37 (~(s(s(s(z))) = s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1782, 442])).
% 1.14/1.37 tff(1784,plain,
% 1.14/1.37 (s(s(z)) = s(s(elem!1))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1709])).
% 1.14/1.37 tff(1785,plain,
% 1.14/1.37 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1784])).
% 1.14/1.37 tff(1786,plain,
% 1.14/1.37 (b(s(s(s(z))), s(s(elem!1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[176, 1785])).
% 1.14/1.37 tff(1787,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.14/1.37 tff(1788,plain,
% 1.14/1.37 (s(s(elem!1)) = s(z)),
% 1.14/1.37 inference(transitivity,[status(thm)],[1787, 1710])).
% 1.14/1.37 tff(1789,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[566, 1788])).
% 1.14/1.37 tff(1790,plain,((~(s(s(elem!1)) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(1791,plain,
% 1.14/1.37 (~(s(s(elem!1)) = s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1790, 442])).
% 1.14/1.37 tff(1792,plain,
% 1.14/1.37 (s(s(elem!1)) = s(s(z))),
% 1.14/1.37 inference(symmetry,[status(thm)],[1784])).
% 1.14/1.37 tff(1793,plain,
% 1.14/1.37 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1792])).
% 1.14/1.37 tff(1794,plain,
% 1.14/1.37 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[1793])).
% 1.14/1.37 tff(1795,plain,
% 1.14/1.37 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[342, 1794])).
% 1.14/1.37 tff(1796,plain,
% 1.14/1.37 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1710])).
% 1.14/1.37 tff(1797,plain,
% 1.14/1.37 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[1796])).
% 1.14/1.37 tff(1798,plain,
% 1.14/1.37 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1709])).
% 1.14/1.37 tff(1799,plain,
% 1.14/1.37 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[1798])).
% 1.14/1.37 tff(1800,plain,
% 1.14/1.37 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1799])).
% 1.14/1.37 tff(1801,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1802,plain,
% 1.14/1.37 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1803,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1802])).
% 1.14/1.37 tff(1804,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[1803, 1801])).
% 1.14/1.37 tff(1805,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1806,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 1.14/1.37 tff(1807,plain,
% 1.14/1.37 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1806, 116, 1766, 28, 1764, 1720])).
% 1.14/1.37 tff(1808,plain,
% 1.14/1.37 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1807, 1800])).
% 1.14/1.37 tff(1809,plain,
% 1.14/1.37 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[325, 1808])).
% 1.14/1.37 tff(1810,plain,
% 1.14/1.37 (r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1809, 1797])).
% 1.14/1.37 tff(1811,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1812,plain,
% 1.14/1.37 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1813,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1812])).
% 1.14/1.37 tff(1814,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[1813, 1811])).
% 1.14/1.37 tff(1815,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1816,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 1.14/1.37 tff(1817,plain,
% 1.14/1.37 ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1816, 77, 1810])).
% 1.14/1.37 tff(1818,plain,
% 1.14/1.37 (~r(s(s(elem!1)), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1817, 1795])).
% 1.14/1.37 tff(1819,plain,
% 1.14/1.37 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[767, 1818, 1791])).
% 1.14/1.37 tff(1820,plain,
% 1.14/1.37 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.14/1.37 inference(commutativity,[status(thm)],[])).
% 1.14/1.37 tff(1821,plain,
% 1.14/1.37 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.14/1.37 inference(symmetry,[status(thm)],[1820])).
% 1.14/1.37 tff(1822,plain,
% 1.14/1.37 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1821])).
% 1.14/1.37 tff(1823,plain,
% 1.14/1.37 (~(s(elem!1) = s(s(elem!1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1791, 1822])).
% 1.14/1.37 tff(1824,plain,
% 1.14/1.37 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1784])).
% 1.14/1.37 tff(1825,plain,
% 1.14/1.37 (r(s(s(elem!1)), elem!1)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1714, 1824])).
% 1.14/1.37 tff(1826,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1827,plain,
% 1.14/1.37 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1828,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1827])).
% 1.14/1.37 tff(1829,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[1828, 1826])).
% 1.14/1.37 tff(1830,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1831,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.14/1.37 tff(1832,plain,
% 1.14/1.37 ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1831, 77, 1825, 1810])).
% 1.14/1.37 tff(1833,plain,
% 1.14/1.37 (~r(s(elem!1), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1832, 1795])).
% 1.14/1.37 tff(1834,plain,
% 1.14/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1835,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1836,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 1.14/1.37 tff(1837,plain,
% 1.14/1.37 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1836, 21, 1833])).
% 1.14/1.37 tff(1838,plain,
% 1.14/1.37 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1837, 1823])).
% 1.14/1.37 tff(1839,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1840,plain,
% 1.14/1.37 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1841,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[1840])).
% 1.14/1.37 tff(1842,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[1841, 1839])).
% 1.14/1.37 tff(1843,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1844,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.14/1.37 tff(1845,plain,
% 1.14/1.37 (~b(s(s(s(z))), s(elem!1))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1844, 116, 1764, 1838, 1819, 1786])).
% 1.14/1.37 tff(1846,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.14/1.37 tff(1847,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.14/1.37 tff(1848,assumption,(~r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.14/1.37 tff(1849,plain,
% 1.14/1.37 (((~![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)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(1850,plain,
% 1.14/1.37 ((~![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)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(1851,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 1.14/1.38 tff(1852,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1851, 21, 1848, 1847, 1846])).
% 1.14/1.38 tff(1853,plain,(b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)) | (s(s(s(z))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(1854,plain,
% 1.14/1.38 (r(s(s(s(z))), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1853, 1845, 1783])).
% 1.14/1.38 tff(1855,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1784])).
% 1.14/1.38 tff(1856,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[344, 1855])).
% 1.14/1.38 tff(1857,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1858,plain,
% 1.14/1.38 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1859,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1858])).
% 1.14/1.38 tff(1860,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1859, 1857])).
% 1.14/1.38 tff(1861,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1862,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 1.14/1.38 tff(1863,plain,
% 1.14/1.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1862, 77, 1856, 1854, 1778])).
% 1.14/1.38 tff(1864,plain,
% 1.14/1.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1146, 1863])).
% 1.14/1.38 tff(1865,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1866,plain,
% 1.14/1.38 (((~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(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1867,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1866])).
% 1.14/1.38 tff(1868,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1867, 1865])).
% 1.14/1.38 tff(1869,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1870,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 1.14/1.38 tff(1871,plain,
% 1.14/1.38 (~b(elem!1, s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1870, 116, 1766, 28, 1864])).
% 1.14/1.38 tff(1872,plain,
% 1.14/1.38 (r(elem!1, s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1345, 1871, 1751])).
% 1.14/1.38 tff(1873,plain,
% 1.14/1.38 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.38 tff(1874,plain,
% 1.14/1.38 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1873, 1093])).
% 1.14/1.38 tff(1875,plain,
% 1.14/1.38 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1874])).
% 1.14/1.38 tff(1876,plain,
% 1.14/1.38 (~(elem!1 = s(s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[508, 1875])).
% 1.14/1.38 tff(1877,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(1878,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.38 tff(1879,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.14/1.38 tff(1880,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1881,plain,
% 1.14/1.38 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1882,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1881])).
% 1.14/1.38 tff(1883,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1882, 1880])).
% 1.14/1.38 tff(1884,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1885,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.14/1.38 tff(1886,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1885, 116, 1879, 846, 1878, 1877])).
% 1.14/1.38 tff(1887,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(1888,plain,
% 1.14/1.38 (~b(elem!1, s(s(elem!1)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1887, 1838, 1764, 1819])).
% 1.14/1.38 tff(1889,plain,
% 1.14/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1890,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1891,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 1.14/1.38 tff(1892,plain,
% 1.14/1.38 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1891, 21])).
% 1.14/1.38 tff(1893,plain,
% 1.14/1.38 (r(elem!1, s(s(elem!1)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1892, 1888, 1876])).
% 1.14/1.38 tff(1894,plain,
% 1.14/1.38 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.38 tff(1895,plain,
% 1.14/1.38 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1894])).
% 1.14/1.38 tff(1896,plain,
% 1.14/1.38 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[895, 1895])).
% 1.14/1.38 tff(1897,plain,
% 1.14/1.38 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1709])).
% 1.14/1.38 tff(1898,plain,
% 1.14/1.38 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1897])).
% 1.14/1.38 tff(1899,plain,
% 1.14/1.38 (s(s(s(s(z)))) = z),
% 1.14/1.38 inference(transitivity,[status(thm)],[554, 825, 47])).
% 1.14/1.38 tff(1900,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[242, 1899])).
% 1.14/1.38 tff(1901,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(1902,plain,
% 1.14/1.38 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1901, 1898])).
% 1.14/1.38 tff(1903,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.14/1.38 tff(1904,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.38 tff(1905,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1906,plain,
% 1.14/1.38 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1907,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1906])).
% 1.14/1.38 tff(1908,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1907, 1905])).
% 1.14/1.38 tff(1909,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1910,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 1.14/1.38 tff(1911,plain,
% 1.14/1.38 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1910, 77, 1904, 1903])).
% 1.14/1.38 tff(1912,plain,
% 1.14/1.38 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[858, 21, 855, 1911])).
% 1.14/1.38 tff(1913,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1914,plain,
% 1.14/1.38 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1915,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1914])).
% 1.14/1.38 tff(1916,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1915, 1913])).
% 1.14/1.38 tff(1917,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1918,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 1.14/1.38 tff(1919,plain,
% 1.14/1.38 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1918, 77, 493, 359, 1904])).
% 1.14/1.38 tff(1920,plain,
% 1.14/1.38 (b(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[885, 1919, 952])).
% 1.14/1.38 tff(1921,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1922,plain,
% 1.14/1.38 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1923,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1922])).
% 1.14/1.38 tff(1924,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1923, 1921])).
% 1.14/1.38 tff(1925,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1926,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.14/1.38 tff(1927,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1926, 116, 1054, 28, 846, 1920, 1912])).
% 1.14/1.38 tff(1928,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(1929,plain,
% 1.14/1.38 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1928, 1766, 28, 1764, 1902, 1896, 1893, 1872, 1742])).
% 1.14/1.38 tff(1930,plain,
% 1.14/1.38 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1380, 1929])).
% 1.14/1.38 tff(1931,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1932,plain,
% 1.14/1.38 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(1933,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[1932])).
% 1.14/1.38 tff(1934,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1933, 1931])).
% 1.14/1.38 tff(1935,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(1936,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.14/1.39 tff(1937,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1936, 116, 28, 1864, 1930])).
% 1.14/1.39 tff(1938,plain,
% 1.14/1.39 (((~![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)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(1939,plain,
% 1.14/1.39 ((~![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)))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(1940,plain,
% 1.14/1.39 ((~![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))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 1.14/1.39 tff(1941,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1940, 21, 1937, 1708])).
% 1.14/1.39 tff(1942,plain,
% 1.14/1.39 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1792])).
% 1.14/1.39 tff(1943,plain,
% 1.14/1.39 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.14/1.39 inference(symmetry,[status(thm)],[1942])).
% 1.14/1.39 tff(1944,plain,
% 1.14/1.39 (b(s(s(elem!1)), s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[27, 1943])).
% 1.14/1.39 tff(1945,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(1946,plain,
% 1.14/1.39 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(1947,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1946])).
% 1.14/1.39 tff(1948,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[1947, 1945])).
% 1.14/1.39 tff(1949,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(1950,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 1.14/1.39 tff(1951,plain,
% 1.14/1.39 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1950, 116, 28, 1864, 1930, 1944])).
% 1.14/1.39 tff(1952,plain,
% 1.14/1.39 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1784])).
% 1.14/1.39 tff(1953,plain,
% 1.14/1.39 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[1952, 1504])).
% 1.14/1.39 tff(1954,plain,
% 1.14/1.39 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1953])).
% 1.14/1.39 tff(1955,plain,
% 1.14/1.39 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1202, 1954])).
% 1.14/1.39 tff(1956,plain,
% 1.14/1.39 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[916, 21, 1955, 1951])).
% 1.14/1.39 tff(1957,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(1958,plain,
% 1.14/1.39 (((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(1959,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1958])).
% 1.14/1.39 tff(1960,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[1959, 1957])).
% 1.14/1.39 tff(1961,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(1962,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1961, 1960])).
% 1.14/1.39 tff(1963,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1962, 77, 1856, 1956, 1941])).
% 1.14/1.39 tff(1964,plain,((~(z = elem!1)) | (~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(z)))) | r(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(1965,plain,
% 1.14/1.39 (~(z = elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1964, 1700, 106, 90, 28, 2])).
% 1.14/1.39 tff(1966,plain,
% 1.14/1.39 (r(s(z), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[172, 167])).
% 1.14/1.39 tff(1967,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[220, 154, 28, 152])).
% 1.14/1.39 tff(1968,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[226, 1967])).
% 1.14/1.39 tff(1969,plain,
% 1.14/1.39 (~r(s(s(s(s(z)))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[237, 1968, 66])).
% 1.14/1.39 tff(1970,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[247, 1969])).
% 1.14/1.39 tff(1971,plain,
% 1.14/1.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[122, 116, 152, 28, 154])).
% 1.14/1.39 tff(1972,plain,
% 1.14/1.39 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[149, 1971])).
% 1.14/1.39 tff(1973,plain,
% 1.14/1.39 (~r(s(z), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[336, 1966, 1972])).
% 1.14/1.39 tff(1974,plain,
% 1.14/1.39 (b(s(z), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[325, 1973])).
% 1.14/1.39 tff(1975,plain,
% 1.14/1.39 (b(elem!1, z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1458, 466, 270])).
% 1.14/1.39 tff(1976,plain,
% 1.14/1.39 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[466])).
% 1.14/1.39 tff(1977,plain,
% 1.14/1.39 (b(elem!1, s(s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[249, 1976])).
% 1.14/1.39 tff(1978,plain,
% 1.14/1.39 (b(z, elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1044, 478, 1052])).
% 1.14/1.39 tff(1979,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1063, 1978, 1977, 254, 1975])).
% 1.14/1.39 tff(1980,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), z)) | r(z, elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(1981,plain,
% 1.14/1.39 (~b(s(z), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1980, 466, 254, 1052, 249])).
% 1.14/1.39 tff(1982,plain,
% 1.14/1.39 (elem!1 = s(z)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[466, 617])).
% 1.14/1.39 tff(1983,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1046, 1982])).
% 1.14/1.39 tff(1984,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(1985,plain,
% 1.14/1.39 (elem!1 = s(z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1984, 466])).
% 1.14/1.39 tff(1986,plain,
% 1.14/1.39 (b(elem!1, z) <=> b(s(z), z)),
% 1.14/1.39 inference(monotonicity,[status(thm)],[417])).
% 1.14/1.39 tff(1987,plain,
% 1.14/1.39 (b(s(z), z) <=> b(elem!1, z)),
% 1.14/1.39 inference(symmetry,[status(thm)],[1986])).
% 1.14/1.39 tff(1988,plain,
% 1.14/1.39 ((~b(s(z), z)) <=> (~b(elem!1, z))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1987])).
% 1.14/1.39 tff(1989,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.14/1.39 tff(1990,plain,
% 1.14/1.39 (~b(elem!1, z)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.14/1.39 tff(1991,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[537, 1990])).
% 1.14/1.39 tff(1992,plain,((~(elem!1 = s(z))) | (~b(elem!1, z)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(1993,plain,
% 1.14/1.39 (~b(elem!1, z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1992, 1985, 1981])).
% 1.14/1.39 tff(1994,plain,
% 1.14/1.39 (r(elem!1, z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[545, 1993, 439])).
% 1.14/1.39 tff(1995,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(1996,plain,
% 1.14/1.39 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(1997,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1996])).
% 1.14/1.39 tff(1998,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[1997, 1995])).
% 1.14/1.39 tff(1999,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2000,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.14/1.39 tff(2001,plain,
% 1.14/1.39 (~r(s(s(elem!1)), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2000, 77, 575, 493])).
% 1.14/1.39 tff(2002,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2001, 1479])).
% 1.14/1.39 tff(2003,plain,((~r(s(s(s(z))), z)) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2004,plain,
% 1.14/1.39 (~r(elem!1, s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2003, 1994, 67, 466])).
% 1.14/1.39 tff(2005,plain,
% 1.14/1.39 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.14/1.39 inference(monotonicity,[status(thm)],[466])).
% 1.14/1.39 tff(2006,plain,
% 1.14/1.39 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2005, 1093])).
% 1.14/1.39 tff(2007,plain,
% 1.14/1.39 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2006])).
% 1.14/1.39 tff(2008,plain,
% 1.14/1.39 (~(elem!1 = s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[566, 2007])).
% 1.14/1.39 tff(2009,plain,
% 1.14/1.39 (b(elem!1, s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1892, 2008, 2004])).
% 1.14/1.39 tff(2010,plain,
% 1.14/1.39 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1474, 1475])).
% 1.14/1.39 tff(2011,plain,
% 1.14/1.39 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[27, 2010])).
% 1.14/1.39 tff(2012,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1475])).
% 1.14/1.39 tff(2013,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[28, 2012])).
% 1.14/1.39 tff(2014,assumption,(~b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.39 tff(2015,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2014, 2013])).
% 1.14/1.39 tff(2016,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(s(z)))), s(s(elem!1))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2017,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2016, 466, 28])).
% 1.14/1.39 tff(2018,plain,
% 1.14/1.39 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1476])).
% 1.14/1.39 tff(2019,plain,
% 1.14/1.39 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.14/1.39 inference(symmetry,[status(thm)],[2018])).
% 1.14/1.39 tff(2020,plain,
% 1.14/1.39 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[1474])).
% 1.14/1.39 tff(2021,plain,
% 1.14/1.39 (b(s(s(s(z))), s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[176, 2020])).
% 1.14/1.39 tff(2022,plain,
% 1.14/1.39 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2021, 2019])).
% 1.14/1.39 tff(2023,assumption,(b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.39 tff(2024,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2025,plain,
% 1.14/1.39 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2026,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2025])).
% 1.14/1.39 tff(2027,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2026, 2024])).
% 1.14/1.39 tff(2028,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2029,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.14/1.39 tff(2030,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2029, 116, 1879, 1054, 1878, 1877, 2023])).
% 1.14/1.39 tff(2031,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2032,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2031, 2022, 1977, 2017, 2011, 2009])).
% 1.14/1.39 tff(2033,plain,((~(s(z) = elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2034,plain,
% 1.14/1.39 (~(s(z) = elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2033, 1974, 154, 152, 67, 534, 28, 1970, 1052])).
% 1.14/1.39 tff(2035,plain,
% 1.14/1.39 (b(s(z), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[357, 2034, 1700])).
% 1.14/1.39 tff(2036,plain,
% 1.14/1.39 (b(s(z), s(s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[847, 372])).
% 1.14/1.39 tff(2037,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[167, 2036])).
% 1.14/1.39 tff(2038,plain,((~(s(s(z)) = elem!1)) | b(s(z), s(s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2039,plain,
% 1.14/1.39 (~(s(s(z)) = elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2038, 167, 2035])).
% 1.14/1.39 tff(2040,plain,
% 1.14/1.39 (b(z, elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1044, 518, 1052])).
% 1.14/1.39 tff(2041,plain,
% 1.14/1.39 (~(elem!1 = s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[420, 2034])).
% 1.14/1.39 tff(2042,plain,
% 1.14/1.39 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.14/1.39 inference(symmetry,[status(thm)],[1752])).
% 1.14/1.39 tff(2043,plain,
% 1.14/1.39 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2042])).
% 1.14/1.39 tff(2044,plain,
% 1.14/1.39 (~(s(s(s(s(z)))) = s(z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[320, 2043])).
% 1.14/1.39 tff(2045,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2046,plain,
% 1.14/1.39 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2047,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2046])).
% 1.14/1.39 tff(2048,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2047, 2045])).
% 1.14/1.39 tff(2049,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2050,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 1.14/1.39 tff(2051,plain,
% 1.14/1.39 (~r(s(s(s(s(z)))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2050, 77, 1968, 1966])).
% 1.14/1.39 tff(2052,plain,
% 1.14/1.39 (((~![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)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2053,plain,
% 1.14/1.39 ((~![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)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2054,plain,
% 1.14/1.39 ((~![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))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 1.14/1.39 tff(2055,plain,
% 1.14/1.39 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2054, 21, 2051])).
% 1.14/1.39 tff(2056,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2055, 2044])).
% 1.14/1.39 tff(2057,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.14/1.39 tff(2058,plain,
% 1.14/1.39 (~r(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1319, 77, 575, 66])).
% 1.14/1.39 tff(2059,plain,
% 1.14/1.39 (b(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[426, 2058, 422])).
% 1.14/1.39 tff(2060,plain,
% 1.14/1.39 (b(elem!1, s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[633, 629, 1046])).
% 1.14/1.39 tff(2061,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2062,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2063,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 1.14/1.39 tff(2064,plain,
% 1.14/1.39 (~b(s(s(z)), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2063, 116, 1055, 847, 2060, 1331])).
% 1.14/1.39 tff(2065,plain,
% 1.14/1.39 (r(s(s(z)), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[25, 2064])).
% 1.14/1.39 tff(2066,plain,
% 1.14/1.39 (~r(s(z), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[162, 77, 155, 2065])).
% 1.14/1.39 tff(2067,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2068,plain,
% 1.14/1.39 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2069,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2068])).
% 1.14/1.39 tff(2070,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2069, 2067])).
% 1.14/1.39 tff(2071,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.14/1.40 inference(quant_inst,[status(thm)],[])).
% 1.14/1.40 tff(2072,plain,
% 1.14/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 1.14/1.40 tff(2073,plain,
% 1.14/1.40 (~b(s(z), s(s(z)))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[2072, 116, 847, 2060, 1331])).
% 1.14/1.40 tff(2074,plain,
% 1.14/1.40 ($false),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[170, 21, 54, 2073, 2066])).
% 1.14/1.40 tff(2075,plain,((~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (elem!1 = s(z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.40 tff(2076,plain,
% 1.14/1.40 (~r(s(z), z)),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[2075, 2059, 847, 1055, 1046, 575])).
% 1.14/1.40 tff(2077,plain,
% 1.14/1.40 (b(s(z), z)),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[210, 2076])).
% 1.14/1.40 tff(2078,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(2079,plain,
% 1.14/1.40 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(2080,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1))))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2079])).
% 1.14/1.40 tff(2081,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.14/1.40 inference(transitivity,[status(thm)],[2080, 2078])).
% 1.14/1.40 tff(2082,plain,
% 1.14/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.14/1.40 inference(quant_inst,[status(thm)],[])).
% 1.14/1.40 tff(2083,plain,
% 1.14/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 1.14/1.40 tff(2084,plain,
% 1.14/1.40 ($false),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[2083, 116, 1055, 847, 270, 667])).
% 1.14/1.40 tff(2085,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.40 tff(2086,plain,
% 1.14/1.40 (~b(elem!1, s(z))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[2085, 2077, 1055, 847])).
% 1.14/1.40 tff(2087,plain,
% 1.14/1.40 (r(elem!1, s(z))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[633, 2086, 1046])).
% 1.14/1.40 tff(2088,plain,
% 1.14/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(2089,plain,
% 1.14/1.40 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2090,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2089])).
% 1.24/1.40 tff(2091,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2090, 2088])).
% 1.24/1.40 tff(2092,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2093,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.24/1.40 tff(2094,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2093, 77, 575, 293, 620])).
% 1.24/1.40 tff(2095,plain,((~r(z, s(z))) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2096,plain,
% 1.24/1.40 (~r(z, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2095, 2087, 575])).
% 1.24/1.40 tff(2097,plain,
% 1.24/1.40 (b(z, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[289, 2096])).
% 1.24/1.40 tff(2098,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2099,plain,
% 1.24/1.40 (((~b(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))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2100,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2099])).
% 1.24/1.40 tff(2101,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.24/1.40 tff(2102,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2103,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.24/1.40 tff(2104,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2103, 116, 2077, 2097, 254, 2057])).
% 1.24/1.40 tff(2105,plain,((~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(s(z)) = elem!1) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2106,plain,
% 1.24/1.40 (~r(elem!1, z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2105, 2056, 1970, 2041, 2040, 2035, 2039, 66])).
% 1.24/1.40 tff(2107,plain,
% 1.24/1.40 (b(elem!1, z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[545, 534, 1050])).
% 1.24/1.40 tff(2108,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2109,plain,
% 1.24/1.40 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2110,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2109])).
% 1.24/1.40 tff(2111,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2110, 2108])).
% 1.24/1.40 tff(2112,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2113,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.24/1.40 tff(2114,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2113, 116, 2040, 2107, 847, 270])).
% 1.24/1.40 tff(2115,plain,((z = elem!1) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2116,plain,
% 1.24/1.40 (~b(s(z), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2115, 2106, 518, 2035, 1052])).
% 1.24/1.40 tff(2117,plain,
% 1.24/1.40 (r(s(z), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[210, 2116])).
% 1.24/1.40 tff(2118,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[162, 77, 2117, 66, 1966])).
% 1.24/1.40 tff(2119,plain,(b(s(z), s(s(z))) | (~r(s(s(z)), z)) | (z = elem!1) | r(z, elem!1) | r(s(z), elem!1) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2120,plain,
% 1.24/1.40 (b(s(z), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2119, 1965, 26, 1052, 1700, 64, 28])).
% 1.24/1.40 tff(2121,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2122,plain,
% 1.24/1.40 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2123,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2122])).
% 1.24/1.40 tff(2124,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2123, 2121])).
% 1.24/1.40 tff(2125,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2126,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 1.24/1.40 tff(2127,plain,
% 1.24/1.40 (~b(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2126, 116, 106, 90, 2120])).
% 1.24/1.40 tff(2128,plain,
% 1.24/1.40 (r(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[402, 21, 135, 2127])).
% 1.24/1.40 tff(2129,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2130,plain,
% 1.24/1.40 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2131,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2130])).
% 1.24/1.40 tff(2132,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2131, 2129])).
% 1.24/1.40 tff(2133,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2134,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 1.24/1.40 tff(2135,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2134, 77, 155, 67, 1047])).
% 1.24/1.40 tff(2136,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2137,plain,
% 1.24/1.40 (~r(s(z), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2136, 2128, 64])).
% 1.24/1.40 tff(2138,plain,
% 1.24/1.40 (b(s(z), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[210, 2137])).
% 1.24/1.40 tff(2139,plain,
% 1.24/1.40 (b(z, elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1044, 1965, 1052])).
% 1.24/1.40 tff(2140,plain,
% 1.24/1.40 (~r(s(s(z)), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[96, 77, 64, 66])).
% 1.24/1.40 tff(2141,plain,
% 1.24/1.40 (b(s(s(z)), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[105, 2140])).
% 1.24/1.40 tff(2142,plain,
% 1.24/1.40 (s(z) = elem!1),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[357, 340, 1700])).
% 1.24/1.40 tff(2143,plain,
% 1.24/1.40 (~r(s(s(s(z))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[85, 64, 66])).
% 1.24/1.40 tff(2144,plain,
% 1.24/1.40 (b(s(s(s(z))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[89, 21, 2143, 56])).
% 1.24/1.40 tff(2145,plain,
% 1.24/1.40 (~b(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2126, 116, 2141, 2144, 174])).
% 1.24/1.40 tff(2146,plain,
% 1.24/1.40 (r(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[402, 21, 135, 2145])).
% 1.24/1.40 tff(2147,plain,
% 1.24/1.40 (~(s(s(z)) = elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[376, 340, 174])).
% 1.24/1.40 tff(2148,plain,
% 1.24/1.40 (~r(s(z), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2136, 2146, 64])).
% 1.24/1.40 tff(2149,plain,
% 1.24/1.40 (b(s(z), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[210, 2148])).
% 1.24/1.40 tff(2150,plain,
% 1.24/1.40 (b(elem!1, z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1458, 2142, 2149])).
% 1.24/1.40 tff(2151,plain,
% 1.24/1.40 (~(elem!1 = s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1470, 2150, 57])).
% 1.24/1.40 tff(2152,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1657, 2151, 2150, 2147, 28, 2144, 66, 2146, 2142, 2141, 1055])).
% 1.24/1.40 tff(2153,plain,(b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(z, elem!1)) | b(s(s(s(z))), z) | (~b(s(z), s(s(z)))) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2154,plain,
% 1.24/1.40 (b(s(z), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2153, 2139, 26, 28, 57, 2120, 1700])).
% 1.24/1.40 tff(2155,plain,
% 1.24/1.40 (r(elem!1, z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2115, 2154, 1965, 2138, 1052])).
% 1.24/1.40 tff(2156,plain,
% 1.24/1.40 (~r(s(s(z)), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1319, 77, 2155, 26])).
% 1.24/1.40 tff(2157,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2158,plain,
% 1.24/1.40 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2159,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2158])).
% 1.24/1.40 tff(2160,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2159, 2157])).
% 1.24/1.40 tff(2161,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2162,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 1.24/1.40 tff(2163,plain,
% 1.24/1.40 (~r(elem!1, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2162, 77, 2155, 64])).
% 1.24/1.40 tff(2164,plain,
% 1.24/1.40 (~b(s(z), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[184, 2120, 90, 106])).
% 1.24/1.40 tff(2165,plain,
% 1.24/1.40 (~(elem!1 = s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1667, 2154, 2164])).
% 1.24/1.40 tff(2166,plain,
% 1.24/1.40 (b(elem!1, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1345, 2165, 2163])).
% 1.24/1.40 tff(2167,plain,
% 1.24/1.40 (~b(s(s(z)), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1340, 2166, 90, 106])).
% 1.24/1.40 tff(2168,plain,
% 1.24/1.40 (s(s(z)) = elem!1),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[426, 2167, 2156])).
% 1.24/1.40 tff(2169,plain,
% 1.24/1.40 (s(s(s(z))) = s(elem!1)),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2168])).
% 1.24/1.40 tff(2170,plain,
% 1.24/1.40 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2169])).
% 1.24/1.40 tff(2171,plain,
% 1.24/1.40 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[2170])).
% 1.24/1.40 tff(2172,plain,
% 1.24/1.40 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2171])).
% 1.24/1.40 tff(2173,plain,
% 1.24/1.40 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.24/1.40 inference(symmetry,[status(thm)],[2172])).
% 1.24/1.40 tff(2174,plain,
% 1.24/1.40 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2173])).
% 1.24/1.40 tff(2175,plain,
% 1.24/1.40 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2168])).
% 1.24/1.40 tff(2176,plain,
% 1.24/1.40 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2175])).
% 1.24/1.40 tff(2177,plain,
% 1.24/1.40 (~b(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[123, 2176])).
% 1.24/1.40 tff(2178,plain,
% 1.24/1.40 (~b(elem!1, s(s(elem!1)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2177, 2174])).
% 1.24/1.40 tff(2179,plain,
% 1.24/1.40 (~(s(s(elem!1)) = elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[529, 2168, 1965])).
% 1.24/1.40 tff(2180,plain,
% 1.24/1.40 (s(s(elem!1)) = elem!1),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[1080, 1092])).
% 1.24/1.40 tff(2181,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[574, 2180])).
% 1.24/1.40 tff(2182,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2183,plain,
% 1.24/1.40 (~(elem!1 = s(s(elem!1)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2182, 2179])).
% 1.24/1.40 tff(2184,plain,
% 1.24/1.40 (~b(elem!1, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2085, 2154, 2139, 2138])).
% 1.24/1.40 tff(2185,plain,
% 1.24/1.40 (~(s(z) = elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[480, 2168])).
% 1.24/1.40 tff(2186,plain,
% 1.24/1.40 (~(elem!1 = s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[420, 2185])).
% 1.24/1.40 tff(2187,plain,
% 1.24/1.40 (r(elem!1, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[633, 2186, 2184])).
% 1.24/1.40 tff(2188,plain,
% 1.24/1.40 (~r(z, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2095, 620, 575])).
% 1.24/1.40 tff(2189,plain,
% 1.24/1.40 (b(z, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[289, 2188])).
% 1.24/1.40 tff(2190,plain,
% 1.24/1.40 (~r(s(s(elem!1)), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[802, 493, 620])).
% 1.24/1.40 tff(2191,plain,
% 1.24/1.40 (b(s(s(elem!1)), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[808, 2190])).
% 1.24/1.40 tff(2192,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2193,plain,
% 1.24/1.41 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2194,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2193])).
% 1.24/1.41 tff(2195,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2194, 2192])).
% 1.24/1.41 tff(2196,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2197,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 1.24/1.41 tff(2198,plain,
% 1.24/1.41 (~b(z, s(s(elem!1)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2197, 116, 1055, 2191, 270, 2189])).
% 1.24/1.41 tff(2199,plain,
% 1.24/1.41 (r(z, s(s(elem!1)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[514, 2198])).
% 1.24/1.41 tff(2200,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2201,plain,
% 1.24/1.41 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2202,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2201])).
% 1.24/1.41 tff(2203,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2202, 2200])).
% 1.24/1.41 tff(2204,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2205,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2204, 2203])).
% 1.24/1.41 tff(2206,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2205, 77, 575, 2199, 493])).
% 1.24/1.41 tff(2207,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2208,plain,
% 1.24/1.41 (~r(elem!1, s(s(elem!1)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2207, 2187, 2139, 2155, 2138])).
% 1.24/1.41 tff(2209,plain,
% 1.24/1.41 (b(elem!1, s(s(elem!1)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1892, 2208, 2183])).
% 1.24/1.41 tff(2210,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2209, 2178])).
% 1.24/1.41 tff(2211,plain,(r(s(z), elem!1) | r(z, elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2212,plain,
% 1.24/1.41 (r(s(z), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2211, 1699, 28, 57, 2])).
% 1.24/1.41 tff(2213,plain,
% 1.24/1.41 (~r(elem!1, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[368, 2212, 1669])).
% 1.24/1.41 tff(2214,plain,
% 1.24/1.41 (b(elem!1, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1345, 2213, 1668])).
% 1.24/1.41 tff(2215,plain,
% 1.24/1.41 (~r(z, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[301, 1669, 1672])).
% 1.24/1.41 tff(2216,plain,
% 1.24/1.41 (b(z, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[289, 2215])).
% 1.24/1.41 tff(2217,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.24/1.41 tff(2218,plain,
% 1.24/1.41 (z = elem!1),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1044, 1052, 2217])).
% 1.24/1.41 tff(2219,plain,
% 1.24/1.41 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2218])).
% 1.24/1.41 tff(2220,plain,
% 1.24/1.41 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.24/1.41 inference(symmetry,[status(thm)],[2219])).
% 1.24/1.41 tff(2221,plain,
% 1.24/1.41 (r(s(z), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2211, 1052, 28, 57, 2])).
% 1.24/1.41 tff(2222,plain,
% 1.24/1.41 (r(s(z), z)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.24/1.41 tff(2223,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[204, 2222])).
% 1.24/1.41 tff(2224,plain,(r(z, elem!1) | b(z, elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2225,plain,
% 1.24/1.41 (b(z, elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2224, 1699, 28, 57, 2])).
% 1.24/1.41 tff(2226,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2227,plain,
% 1.24/1.41 (((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2228,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2227])).
% 1.24/1.41 tff(2229,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.24/1.41 tff(2230,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2231,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.24/1.41 tff(2232,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2231, 116, 2225, 1660, 2216, 2214, 90])).
% 1.24/1.41 tff(2233,plain,(b(s(s(s(z))), z) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2234,plain,
% 1.24/1.41 (b(s(s(s(z))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2233, 28, 2])).
% 1.24/1.41 tff(2235,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.24/1.41 tff(2236,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2237,plain,
% 1.24/1.41 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2238,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2237])).
% 1.24/1.41 tff(2239,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2238, 2236])).
% 1.24/1.41 tff(2240,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2241,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2240, 2239])).
% 1.24/1.41 tff(2242,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2241, 77, 66, 2235, 291])).
% 1.24/1.41 tff(2243,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2244,plain,
% 1.24/1.41 (~r(z, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2243, 2235, 66])).
% 1.24/1.41 tff(2245,plain,
% 1.24/1.41 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[267, 21, 2244])).
% 1.24/1.41 tff(2246,plain,
% 1.24/1.41 (b(z, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2245, 253])).
% 1.24/1.41 tff(2247,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.41 tff(2248,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2249,plain,
% 1.24/1.41 (((~b(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(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))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2250,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2249])).
% 1.24/1.41 tff(2251,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2250, 2248])).
% 1.24/1.41 tff(2252,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2253,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 1.24/1.41 tff(2254,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2253, 116, 2247, 255, 28, 254])).
% 1.24/1.41 tff(2255,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2256,plain,
% 1.24/1.41 (~b(s(s(s(s(z)))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2255, 2246, 28, 2247])).
% 1.24/1.41 tff(2257,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[247, 2256])).
% 1.24/1.41 tff(2258,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2259,plain,
% 1.24/1.41 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2260,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2259])).
% 1.24/1.41 tff(2261,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2260, 2258])).
% 1.24/1.41 tff(2262,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2263,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 1.24/1.41 tff(2264,plain,
% 1.24/1.41 (~r(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2263, 77, 155, 66])).
% 1.24/1.41 tff(2265,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[237, 228, 66])).
% 1.24/1.41 tff(2266,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[226, 2265])).
% 1.24/1.41 tff(2267,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2268,plain,
% 1.24/1.41 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2269,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2268])).
% 1.24/1.41 tff(2270,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2269, 2267])).
% 1.24/1.41 tff(2271,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2272,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.24/1.41 tff(2273,plain,
% 1.24/1.41 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2272, 116, 2266, 1048, 174])).
% 1.24/1.41 tff(2274,plain,
% 1.24/1.41 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[323, 21, 320, 2273])).
% 1.24/1.41 tff(2275,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2276,plain,
% 1.24/1.41 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2277,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2276])).
% 1.24/1.41 tff(2278,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2277, 2275])).
% 1.24/1.41 tff(2279,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2280,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 1.24/1.41 tff(2281,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2280, 77, 155, 228, 2274])).
% 1.24/1.41 tff(2282,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2283,plain,
% 1.24/1.41 (~b(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2282, 173, 66, 228, 155])).
% 1.24/1.41 tff(2284,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[391, 21, 2283, 388, 2264])).
% 1.24/1.41 tff(2285,plain,((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2286,plain,
% 1.24/1.41 (~r(s(z), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2285, 2257, 66])).
% 1.24/1.41 tff(2287,plain,
% 1.24/1.41 (b(s(z), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[210, 2286])).
% 1.24/1.41 tff(2288,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2289,plain,
% 1.24/1.41 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2290,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2289])).
% 1.24/1.42 tff(2291,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2290, 2288])).
% 1.24/1.42 tff(2292,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2293,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.24/1.42 tff(2294,plain,
% 1.24/1.42 (~b(s(z), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2293, 116, 2287, 2247, 2246])).
% 1.24/1.42 tff(2295,plain,
% 1.24/1.42 (r(s(z), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[194, 2294])).
% 1.24/1.42 tff(2296,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2297,plain,
% 1.24/1.42 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2298,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2297])).
% 1.24/1.42 tff(2299,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2298, 2296])).
% 1.24/1.42 tff(2300,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2301,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 1.24/1.42 tff(2302,plain,
% 1.24/1.42 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2301, 77, 66, 2235, 1904])).
% 1.24/1.42 tff(2303,plain,
% 1.24/1.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 2302])).
% 1.24/1.42 tff(2304,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2305,plain,
% 1.24/1.42 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2306,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2305])).
% 1.24/1.42 tff(2307,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2306, 2304])).
% 1.24/1.42 tff(2308,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2309,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 1.24/1.42 tff(2310,plain,
% 1.24/1.42 (~r(s(z), s(s(s(s(s(z))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2309, 77, 292, 1904])).
% 1.24/1.42 tff(2311,plain,
% 1.24/1.42 (b(s(z), s(s(s(s(s(z))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[870, 21, 1901, 2310])).
% 1.24/1.42 tff(2312,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2313,plain,
% 1.24/1.42 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2314,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2313])).
% 1.24/1.42 tff(2315,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2314, 2312])).
% 1.24/1.42 tff(2316,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2317,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 1.24/1.42 tff(2318,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2317, 77, 2235, 292, 156])).
% 1.24/1.42 tff(2319,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2320,plain,
% 1.24/1.42 (~r(s(z), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2319, 292, 2235])).
% 1.24/1.42 tff(2321,plain,
% 1.24/1.42 (b(s(z), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[172, 2320])).
% 1.24/1.42 tff(2322,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2323,plain,
% 1.24/1.42 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2324,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2323])).
% 1.24/1.42 tff(2325,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2324, 2322])).
% 1.24/1.42 tff(2326,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2327,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 1.24/1.42 tff(2328,plain,
% 1.24/1.42 (~r(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2327, 77, 2235, 292])).
% 1.24/1.42 tff(2329,plain,
% 1.24/1.42 (b(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[391, 21, 388, 2328])).
% 1.24/1.42 tff(2330,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2331,plain,
% 1.24/1.42 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2332,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2331])).
% 1.24/1.42 tff(2333,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2332, 2330])).
% 1.24/1.42 tff(2334,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2335,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 1.24/1.42 tff(2336,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2335, 116, 2329, 2321, 2311, 2303])).
% 1.24/1.42 tff(2337,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2338,plain,
% 1.24/1.42 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2337, 2235, 66, 2295])).
% 1.24/1.42 tff(2339,plain,
% 1.24/1.42 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1380, 2338])).
% 1.24/1.42 tff(2340,plain,
% 1.24/1.42 (~r(s(z), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2319, 2295, 2235])).
% 1.24/1.42 tff(2341,plain,
% 1.24/1.42 (b(s(z), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[172, 2340])).
% 1.24/1.42 tff(2342,plain,
% 1.24/1.42 (~r(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2327, 77, 2235, 2295])).
% 1.24/1.42 tff(2343,plain,
% 1.24/1.42 (b(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[391, 21, 388, 2342])).
% 1.24/1.42 tff(2344,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[237, 2257, 66])).
% 1.24/1.42 tff(2345,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[226, 2344])).
% 1.24/1.42 tff(2346,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2347,plain,
% 1.24/1.42 (((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2348,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2347])).
% 1.24/1.42 tff(2349,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2348, 2346])).
% 1.24/1.42 tff(2350,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2351,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 1.24/1.42 tff(2352,plain,
% 1.24/1.42 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2351, 116, 2287, 2345, 2343, 2341])).
% 1.24/1.42 tff(2353,plain,
% 1.24/1.42 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[325, 2352])).
% 1.24/1.42 tff(2354,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2355,plain,
% 1.24/1.42 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2356,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(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)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2355])).
% 1.24/1.42 tff(2357,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2356, 2354])).
% 1.24/1.42 tff(2358,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2359,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 1.24/1.43 tff(2360,plain,
% 1.24/1.43 (~b(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2359, 116, 2247, 2246, 28])).
% 1.24/1.43 tff(2361,plain,
% 1.24/1.43 (r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1576, 21, 2360, 1563])).
% 1.24/1.43 tff(2362,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2363,plain,
% 1.24/1.43 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2364,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2363])).
% 1.24/1.43 tff(2365,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2364, 2362])).
% 1.24/1.43 tff(2366,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2367,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 1.24/1.43 tff(2368,plain,
% 1.24/1.43 (~r(z, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2367, 77, 2361, 2353])).
% 1.24/1.43 tff(2369,plain,
% 1.24/1.43 (b(z, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[289, 2368])).
% 1.24/1.43 tff(2370,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, 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(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, 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(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2371,plain,
% 1.24/1.43 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, 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(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2372,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, 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(z))))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2371])).
% 1.24/1.43 tff(2373,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, 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(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2372, 2370])).
% 1.24/1.43 tff(2374,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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))))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2375,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, 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(z))))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.24/1.43 tff(2376,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)],[2375, 116, 2369, 2247, 28, 2339])).
% 1.24/1.43 tff(2377,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)],[1940, 21, 2376, 1708])).
% 1.24/1.43 tff(2378,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2379,plain,
% 1.24/1.43 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2380,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2379])).
% 1.24/1.43 tff(2381,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2380, 2378])).
% 1.24/1.43 tff(2382,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2383,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2382, 2381])).
% 1.24/1.43 tff(2384,plain,
% 1.24/1.43 (~b(s(s(s(s(s(z))))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2383, 116, 2369, 2247, 2246, 2339])).
% 1.24/1.43 tff(2385,plain,
% 1.24/1.43 (r(s(s(s(s(s(z))))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[898, 21, 895, 2384])).
% 1.24/1.43 tff(2386,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2387,plain,
% 1.24/1.43 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2388,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2387])).
% 1.24/1.43 tff(2389,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2388, 2386])).
% 1.24/1.43 tff(2390,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2391,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 1.24/1.43 tff(2392,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2391, 77, 2257, 2385, 2377])).
% 1.24/1.43 tff(2393,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2394,plain,
% 1.24/1.43 (~r(s(s(z)), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2393, 2234, 28, 26])).
% 1.24/1.43 tff(2395,plain,
% 1.24/1.43 (b(s(s(z)), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[105, 2394])).
% 1.24/1.43 tff(2396,plain,
% 1.24/1.43 (r(z, elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1044, 446, 2217])).
% 1.24/1.43 tff(2397,plain,
% 1.24/1.43 (~r(s(s(z)), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[456, 2396, 26])).
% 1.24/1.43 tff(2398,plain,
% 1.24/1.43 (~r(s(z), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[164, 156, 26])).
% 1.24/1.43 tff(2399,plain,
% 1.24/1.43 (b(s(z), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[210, 2398])).
% 1.24/1.43 tff(2400,plain,
% 1.24/1.43 ((~b(elem!1, z)) <=> (~b(s(s(z)), z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[536])).
% 1.24/1.43 tff(2401,plain,
% 1.24/1.43 (~b(s(s(z)), z)),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1455, 2400])).
% 1.24/1.43 tff(2402,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1303, 2401])).
% 1.24/1.43 tff(2403,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(z)), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2404,plain,
% 1.24/1.43 (~(s(s(z)) = elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2403, 1303, 1455])).
% 1.24/1.43 tff(2405,plain,
% 1.24/1.43 (b(elem!1, z)),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2247, 1466])).
% 1.24/1.43 tff(2406,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1455, 2405])).
% 1.24/1.43 tff(2407,plain,((~(elem!1 = s(s(s(z))))) | b(elem!1, z) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2408,plain,
% 1.24/1.43 (~(elem!1 = s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2407, 2247, 1455])).
% 1.24/1.43 tff(2409,plain,
% 1.24/1.43 (b(s(s(z)), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[426, 422, 1674])).
% 1.24/1.43 tff(2410,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.43 tff(2411,plain,
% 1.24/1.43 (s(elem!1) = s(z)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[404])).
% 1.24/1.43 tff(2412,plain,
% 1.24/1.43 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2411])).
% 1.24/1.43 tff(2413,plain,
% 1.24/1.43 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.24/1.43 inference(symmetry,[status(thm)],[2412])).
% 1.24/1.43 tff(2414,plain,
% 1.24/1.43 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2413])).
% 1.24/1.43 tff(2415,plain,
% 1.24/1.43 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[404])).
% 1.24/1.43 tff(2416,plain,
% 1.24/1.43 (~(s(s(s(s(z)))) = elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1584, 1362])).
% 1.24/1.43 tff(2417,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[404])).
% 1.24/1.43 tff(2418,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.43 tff(2419,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2418, 2417])).
% 1.24/1.43 tff(2420,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[240, 2419])).
% 1.24/1.43 tff(2421,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2422,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2421, 240, 404])).
% 1.24/1.43 tff(2423,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1596, 2422, 2416])).
% 1.24/1.43 tff(2424,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2425,plain,
% 1.24/1.43 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2426,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2425])).
% 1.24/1.43 tff(2427,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2426, 2424])).
% 1.24/1.43 tff(2428,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2429,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 1.24/1.43 tff(2430,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2429, 116, 1054, 1331, 2410, 1725])).
% 1.24/1.43 tff(2431,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2432,plain,
% 1.24/1.43 (~b(elem!1, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2431, 2423, 1331, 2410])).
% 1.24/1.43 tff(2433,plain,
% 1.24/1.43 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1068, 2432, 1362])).
% 1.24/1.43 tff(2434,plain,
% 1.24/1.43 (z = elem!1),
% 1.24/1.43 inference(symmetry,[status(thm)],[404])).
% 1.24/1.43 tff(2435,plain,
% 1.24/1.43 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2434])).
% 1.24/1.43 tff(2436,plain,
% 1.24/1.43 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[2435])).
% 1.24/1.43 tff(2437,plain,
% 1.24/1.43 (r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[429, 2436])).
% 1.24/1.43 tff(2438,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.43 tff(2439,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2438, 2437])).
% 1.24/1.43 tff(2440,plain,(r(z, s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2441,plain,
% 1.24/1.43 (r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2440, 2433, 404])).
% 1.24/1.43 tff(2442,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.24/1.43 tff(2443,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2444,plain,
% 1.24/1.43 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2445,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2444])).
% 1.24/1.43 tff(2446,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2445, 2443])).
% 1.24/1.43 tff(2447,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2448,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 1.24/1.43 tff(2449,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2448, 116, 2247, 2410, 28, 2442, 254])).
% 1.24/1.43 tff(2450,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2451,plain,
% 1.24/1.43 (~b(z, s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2450, 447, 28, 2247, 2410])).
% 1.24/1.43 tff(2452,plain,
% 1.24/1.43 (r(z, s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1174, 2451])).
% 1.24/1.43 tff(2453,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.43 tff(2454,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2455,plain,
% 1.24/1.43 (((~r(s(s(s(z))), s(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)))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2456,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2455])).
% 1.24/1.43 tff(2457,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2456, 2454])).
% 1.24/1.43 tff(2458,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2459,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 1.24/1.43 tff(2460,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2459, 77, 2453, 1564, 291])).
% 1.24/1.43 tff(2461,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,[]))).
% 1.24/1.44 tff(2462,plain,
% 1.24/1.44 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2461, 291, 1564])).
% 1.24/1.44 tff(2463,plain,
% 1.24/1.44 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1146, 2462])).
% 1.24/1.44 tff(2464,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1572, 1564, 1212])).
% 1.24/1.44 tff(2465,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[226, 2464])).
% 1.24/1.44 tff(2466,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2467,plain,
% 1.24/1.44 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2468,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2467])).
% 1.24/1.44 tff(2469,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2468, 2466])).
% 1.24/1.44 tff(2470,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2471,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 1.24/1.44 tff(2472,plain,
% 1.24/1.44 (~b(s(s(z)), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2471, 116, 2465, 1303, 2410, 2463])).
% 1.24/1.44 tff(2473,plain,
% 1.24/1.44 (r(s(s(z)), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[105, 2472])).
% 1.24/1.44 tff(2474,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2475,plain,
% 1.24/1.44 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2476,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2475])).
% 1.24/1.44 tff(2477,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2476, 2474])).
% 1.24/1.44 tff(2478,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2479,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 1.24/1.44 tff(2480,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2479, 77, 2473, 1212, 291])).
% 1.24/1.44 tff(2481,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2482,plain,
% 1.24/1.44 (~r(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2481, 2452, 1303, 2410, 2441])).
% 1.24/1.44 tff(2483,plain,
% 1.24/1.44 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2434])).
% 1.24/1.44 tff(2484,plain,
% 1.24/1.44 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[2483])).
% 1.24/1.44 tff(2485,plain,
% 1.24/1.44 (r(z, s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[359, 2484])).
% 1.24/1.44 tff(2486,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(2487,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2486, 2485])).
% 1.24/1.44 tff(2488,plain,(r(z, s(s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2489,plain,
% 1.24/1.44 (~r(elem!1, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2488, 2482, 404])).
% 1.24/1.44 tff(2490,plain,
% 1.24/1.44 (b(elem!1, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1345, 2489, 1620])).
% 1.24/1.44 tff(2491,plain,
% 1.24/1.44 (b(z, s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2490, 2415])).
% 1.24/1.44 tff(2492,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2253, 116, 2247, 2491, 28, 447])).
% 1.24/1.44 tff(2493,plain,(r(s(s(s(s(z)))), z) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = z)) | (elem!1 = s(s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2494,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2493, 404, 28, 2247, 1620, 1303, 2410, 1362, 1331])).
% 1.24/1.44 tff(2495,plain,
% 1.24/1.44 ((~b(s(z), elem!1)) <=> (~b(s(z), z))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[405])).
% 1.24/1.44 tff(2496,plain,
% 1.24/1.44 (~b(s(z), z)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[340, 2495])).
% 1.24/1.44 tff(2497,plain,
% 1.24/1.44 (r(s(z), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[210, 2496])).
% 1.24/1.44 tff(2498,plain,
% 1.24/1.44 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2280, 77, 2497, 2494])).
% 1.24/1.44 tff(2499,plain,
% 1.24/1.44 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[323, 21, 320, 2498])).
% 1.24/1.44 tff(2500,plain,
% 1.24/1.44 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[2415])).
% 1.24/1.44 tff(2501,plain,
% 1.24/1.44 ((~b(z, s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2500])).
% 1.24/1.44 tff(2502,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2503,plain,
% 1.24/1.44 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2504,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2503])).
% 1.24/1.44 tff(2505,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2504, 2502])).
% 1.24/1.44 tff(2506,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2507,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2506, 2505])).
% 1.24/1.44 tff(2508,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2507, 116, 2247, 255, 1303])).
% 1.24/1.44 tff(2509,plain,
% 1.24/1.44 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[89, 21, 2508, 56])).
% 1.24/1.44 tff(2510,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2511,plain,
% 1.24/1.44 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2512,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2511])).
% 1.24/1.44 tff(2513,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2512, 2510])).
% 1.24/1.44 tff(2514,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2515,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 1.24/1.44 tff(2516,plain,
% 1.24/1.44 (~r(s(z), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2515, 77, 2509, 156])).
% 1.24/1.44 tff(2517,plain,
% 1.24/1.44 (b(s(z), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[194, 2516])).
% 1.24/1.44 tff(2518,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2519,plain,
% 1.24/1.44 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(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(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2520,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z), s(s(s(s(z))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2519])).
% 1.24/1.44 tff(2521,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2520, 2518])).
% 1.24/1.44 tff(2522,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2523,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 1.24/1.44 tff(2524,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2523, 116, 2247, 255, 28, 2517, 249])).
% 1.24/1.44 tff(2525,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2526,plain,
% 1.24/1.44 (~b(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2525, 2499, 28, 2247, 156, 1303])).
% 1.24/1.44 tff(2527,plain,
% 1.24/1.44 (~b(elem!1, s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2526, 2501])).
% 1.24/1.44 tff(2528,plain,
% 1.24/1.44 (r(elem!1, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1345, 2527, 1620])).
% 1.24/1.44 tff(2529,plain,
% 1.24/1.44 (r(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2488, 2528, 404])).
% 1.24/1.44 tff(2530,plain,
% 1.24/1.44 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[404])).
% 1.24/1.44 tff(2531,plain,
% 1.24/1.44 (b(z, s(s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1054, 2530])).
% 1.24/1.44 tff(2532,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2533,plain,
% 1.24/1.44 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2534,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2533])).
% 1.24/1.44 tff(2535,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2534, 2532])).
% 1.24/1.44 tff(2536,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2537,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 1.24/1.44 tff(2538,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2537, 116, 212, 1054, 1331, 2410])).
% 1.24/1.44 tff(2539,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2540,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2539, 1054, 1331, 2410])).
% 1.24/1.44 tff(2541,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[226, 2540])).
% 1.24/1.44 tff(2542,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2543,plain,
% 1.24/1.44 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2544,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2543])).
% 1.24/1.44 tff(2545,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2544, 2542])).
% 1.24/1.44 tff(2546,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2547,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 1.24/1.44 tff(2548,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2547, 77, 229, 1212, 228])).
% 1.24/1.44 tff(2549,plain,((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2550,plain,
% 1.24/1.44 (~r(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2549, 2541, 228])).
% 1.24/1.44 tff(2551,plain,
% 1.24/1.44 (b(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1174, 2550])).
% 1.24/1.44 tff(2552,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2553,plain,
% 1.24/1.44 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2554,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2553])).
% 1.24/1.44 tff(2555,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2554, 2552])).
% 1.24/1.45 tff(2556,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2557,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.24/1.45 tff(2558,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2557, 116, 2247, 2410, 28, 2551, 2531])).
% 1.24/1.45 tff(2559,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2560,plain,
% 1.24/1.45 (~b(elem!1, s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2559, 404, 2410, 28, 2247, 2494, 1331])).
% 1.24/1.45 tff(2561,plain,
% 1.24/1.45 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1068, 2560, 1362])).
% 1.24/1.45 tff(2562,plain,
% 1.24/1.45 (r(z, s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2440, 2561, 404])).
% 1.24/1.45 tff(2563,plain,
% 1.24/1.45 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2461, 2562, 2529])).
% 1.24/1.45 tff(2564,plain,
% 1.24/1.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1146, 2563])).
% 1.24/1.45 tff(2565,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2566,plain,
% 1.24/1.45 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2567,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2566])).
% 1.24/1.45 tff(2568,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.24/1.45 tff(2569,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2570,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.24/1.45 tff(2571,plain,
% 1.24/1.45 (~b(s(s(s(z))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2570, 116, 2247, 28, 2564, 2499])).
% 1.24/1.45 tff(2572,plain,
% 1.24/1.45 (~b(s(s(s(z))), s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2571, 2414])).
% 1.24/1.45 tff(2573,plain,
% 1.24/1.45 (z = elem!1),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[533, 404])).
% 1.24/1.45 tff(2574,plain,
% 1.24/1.45 (~(s(s(s(z))) = s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1782, 2573])).
% 1.24/1.45 tff(2575,plain,
% 1.24/1.45 (~(s(s(elem!1)) = s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1790, 2573])).
% 1.24/1.45 tff(2576,plain,
% 1.24/1.45 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2411])).
% 1.24/1.45 tff(2577,plain,
% 1.24/1.45 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[2576])).
% 1.24/1.45 tff(2578,plain,
% 1.24/1.45 (s(s(elem!1)) = s(s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2411])).
% 1.24/1.45 tff(2579,plain,
% 1.24/1.45 (s(s(z)) = s(s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[2578])).
% 1.24/1.45 tff(2580,plain,
% 1.24/1.45 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2579])).
% 1.24/1.45 tff(2581,plain,
% 1.24/1.45 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2580, 2577])).
% 1.24/1.45 tff(2582,plain,
% 1.24/1.45 ((~b(s(s(z)), s(z))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2581])).
% 1.24/1.45 tff(2583,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2584,plain,
% 1.24/1.45 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2585,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2584])).
% 1.24/1.45 tff(2586,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2585, 2583])).
% 1.24/1.45 tff(2587,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2588,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 1.24/1.45 tff(2589,plain,
% 1.24/1.45 (~b(s(s(z)), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2588, 116, 2247, 2410, 28, 2499])).
% 1.24/1.45 tff(2590,plain,
% 1.24/1.45 (~b(s(s(elem!1)), s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2589, 2582])).
% 1.24/1.45 tff(2591,plain,
% 1.24/1.45 (r(s(s(elem!1)), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[767, 2590, 2575])).
% 1.24/1.45 tff(2592,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2593,plain,
% 1.24/1.45 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2594,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2593])).
% 1.24/1.45 tff(2595,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2594, 2592])).
% 1.24/1.45 tff(2596,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2597,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 1.24/1.45 tff(2598,plain,
% 1.24/1.45 (~b(s(s(z)), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2597, 116, 2247, 2410, 28, 2564])).
% 1.24/1.45 tff(2599,plain,
% 1.24/1.45 (r(s(s(z)), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[105, 2598])).
% 1.24/1.45 tff(2600,plain,
% 1.24/1.45 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1792])).
% 1.24/1.45 tff(2601,plain,
% 1.24/1.45 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[2600])).
% 1.24/1.45 tff(2602,plain,
% 1.24/1.45 (r(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2235, 2601])).
% 1.24/1.45 tff(2603,assumption,(~r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(2604,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2603, 2602])).
% 1.24/1.45 tff(2605,plain,(r(s(s(elem!1)), s(s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2606,plain,
% 1.24/1.45 (r(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2605, 2599, 2573])).
% 1.24/1.45 tff(2607,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(2608,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(2609,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(2610,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2611,plain,
% 1.24/1.45 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2612,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2611])).
% 1.24/1.45 tff(2613,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2612, 2610])).
% 1.24/1.45 tff(2614,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2615,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 1.24/1.45 tff(2616,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2615, 77, 2609, 2608, 2607])).
% 1.24/1.45 tff(2617,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2618,plain,
% 1.24/1.45 (~r(s(s(s(z))), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2617, 2606, 2591])).
% 1.24/1.45 tff(2619,plain,
% 1.24/1.45 (b(s(s(s(z))), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1853, 2618, 2574])).
% 1.24/1.45 tff(2620,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2619, 2572])).
% 1.24/1.45 tff(2621,plain,((~(elem!1 = z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2622,plain,
% 1.24/1.45 (~(elem!1 = z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2621, 2410, 2247, 28, 1362, 1331, 2408, 156, 1303, 340])).
% 1.24/1.45 tff(2623,plain,
% 1.24/1.45 (r(elem!1, z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[545, 2622, 1455])).
% 1.24/1.45 tff(2624,plain,
% 1.24/1.45 (~(z = elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[445, 2622])).
% 1.24/1.45 tff(2625,plain,
% 1.24/1.45 (b(z, elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1044, 2624, 1052])).
% 1.24/1.45 tff(2626,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2627,plain,
% 1.24/1.45 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2628,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2627])).
% 1.24/1.45 tff(2629,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2628, 2626])).
% 1.24/1.45 tff(2630,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2631,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 1.24/1.45 tff(2632,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2631, 116, 1055, 1054, 1331, 2410, 254])).
% 1.24/1.45 tff(2633,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2634,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2633, 1331, 1054, 1055, 2410])).
% 1.24/1.45 tff(2635,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[247, 2634])).
% 1.24/1.45 tff(2636,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2539, 1331, 1054, 2410])).
% 1.24/1.45 tff(2637,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[225, 2636, 141])).
% 1.24/1.45 tff(2638,plain,
% 1.24/1.45 (~r(s(s(z)), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[237, 2637, 2635])).
% 1.24/1.45 tff(2639,plain,
% 1.24/1.45 (b(s(s(z)), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[25, 2638])).
% 1.24/1.45 tff(2640,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.24/1.45 tff(2641,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2431, 1331, 1054, 2410])).
% 1.24/1.45 tff(2642,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1596, 2641, 2640])).
% 1.24/1.45 tff(2643,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2644,plain,
% 1.24/1.45 (((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2645,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2644])).
% 1.24/1.45 tff(2646,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2645, 2643])).
% 1.24/1.45 tff(2647,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2648,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 1.24/1.45 tff(2649,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2648, 77, 575, 228, 2418])).
% 1.24/1.45 tff(2650,plain,((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2651,plain,
% 1.24/1.45 (~r(elem!1, z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2650, 2635, 2642])).
% 1.24/1.45 tff(2652,plain,
% 1.24/1.45 (b(elem!1, z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[545, 2651, 439])).
% 1.24/1.45 tff(2653,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2654,plain,
% 1.24/1.45 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2655,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2654])).
% 1.24/1.46 tff(2656,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2655, 2653])).
% 1.24/1.46 tff(2657,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2658,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 1.24/1.46 tff(2659,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2658, 116, 1055, 2652, 2639, 1331])).
% 1.24/1.46 tff(2660,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (elem!1 = z) | (s(s(s(s(z)))) = s(s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(2661,plain,
% 1.24/1.46 ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (elem!1 = z) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2660, 137])).
% 1.24/1.46 tff(2662,plain,
% 1.24/1.46 (~b(elem!1, s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2661, 2625, 2410, 2622, 1331, 2416])).
% 1.24/1.46 tff(2663,plain,
% 1.24/1.46 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1068, 2662, 1362])).
% 1.24/1.46 tff(2664,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2665,plain,
% 1.24/1.46 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2666,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2665])).
% 1.24/1.46 tff(2667,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2666, 2664])).
% 1.24/1.46 tff(2668,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2669,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.24/1.46 tff(2670,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2669, 77, 575, 429, 228])).
% 1.24/1.46 tff(2671,plain,((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(2672,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2671, 2663, 2623])).
% 1.24/1.46 tff(2673,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[247, 2672])).
% 1.24/1.46 tff(2674,plain,
% 1.24/1.46 (~b(z, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2450, 2673, 28, 2247, 2410])).
% 1.24/1.46 tff(2675,plain,
% 1.24/1.46 (r(z, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1174, 2674])).
% 1.24/1.46 tff(2676,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2677,plain,
% 1.24/1.46 (((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2678,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2677])).
% 1.24/1.46 tff(2679,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2678, 2676])).
% 1.24/1.46 tff(2680,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2681,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 1.24/1.46 tff(2682,plain,
% 1.24/1.46 (~r(s(z), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2681, 77, 2675, 156])).
% 1.24/1.46 tff(2683,plain,
% 1.24/1.46 (b(s(z), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[210, 2682])).
% 1.24/1.46 tff(2684,plain,
% 1.24/1.46 (~(s(z) = elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1458, 2683, 1455])).
% 1.24/1.46 tff(2685,plain,
% 1.24/1.46 (~(elem!1 = s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[420, 2684])).
% 1.24/1.46 tff(2686,plain,
% 1.24/1.46 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[591])).
% 1.24/1.46 tff(2687,plain,
% 1.24/1.46 (~(s(s(s(z))) = elem!1)),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2408, 2686])).
% 1.24/1.46 tff(2688,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.24/1.46 tff(2689,plain,
% 1.24/1.46 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.24/1.46 inference(commutativity,[status(thm)],[])).
% 1.24/1.46 tff(2690,plain,
% 1.24/1.46 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.24/1.46 inference(symmetry,[status(thm)],[2689])).
% 1.24/1.46 tff(2691,plain,
% 1.24/1.46 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2690])).
% 1.24/1.46 tff(2692,plain,
% 1.24/1.46 (~(s(s(z)) = s(z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[54, 2691])).
% 1.24/1.46 tff(2693,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2694,plain,
% 1.24/1.46 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2695,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2694])).
% 1.24/1.46 tff(2696,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2695, 2693])).
% 1.24/1.46 tff(2697,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2698,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2697, 2696])).
% 1.24/1.46 tff(2699,plain,
% 1.24/1.46 (~b(s(s(z)), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2698, 116, 270, 2189, 1303])).
% 1.24/1.46 tff(2700,plain,
% 1.24/1.46 ((s(s(z)) = s(z)) | r(s(s(z)), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[391, 21, 2699])).
% 1.24/1.46 tff(2701,plain,
% 1.24/1.46 (r(s(s(z)), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2700, 2692])).
% 1.24/1.46 tff(2702,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2703,plain,
% 1.24/1.46 (((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2704,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2703])).
% 1.24/1.46 tff(2705,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2704, 2702])).
% 1.24/1.46 tff(2706,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2707,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 1.24/1.46 tff(2708,plain,
% 1.24/1.46 (~r(s(s(z)), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2707, 77, 575, 620, 2701])).
% 1.24/1.46 tff(2709,plain,
% 1.24/1.46 (b(s(s(z)), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[426, 2708, 422])).
% 1.24/1.46 tff(2710,plain,
% 1.24/1.46 (~r(elem!1, s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2162, 77, 575, 67])).
% 1.24/1.46 tff(2711,plain,
% 1.24/1.46 (b(elem!1, s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1345, 2710, 1620])).
% 1.24/1.46 tff(2712,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2713,plain,
% 1.24/1.46 (((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2714,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2713])).
% 1.24/1.46 tff(2715,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2714, 2712])).
% 1.24/1.46 tff(2716,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2717,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 1.24/1.46 tff(2718,plain,
% 1.24/1.46 (~r(s(s(s(z))), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2717, 77, 575, 67])).
% 1.24/1.46 tff(2719,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.24/1.46 tff(2720,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.24/1.46 tff(2721,plain,
% 1.24/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2722,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2723,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2722, 2721])).
% 1.24/1.46 tff(2724,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2723, 21, 2720, 2719, 2688])).
% 1.24/1.46 tff(2725,plain,(b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(2726,plain,
% 1.24/1.46 (b(s(s(s(z))), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2725, 2718, 2688])).
% 1.24/1.46 tff(2727,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2728,plain,
% 1.24/1.46 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2729,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2728])).
% 1.24/1.46 tff(2730,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2729, 2727])).
% 1.24/1.46 tff(2731,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2732,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.24/1.46 tff(2733,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2732, 116, 1055, 2726, 2711, 1303, 1331])).
% 1.24/1.46 tff(2734,plain,((~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(2735,plain,
% 1.24/1.46 (~r(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2734, 2709, 1303, 1055, 2688, 1620, 575])).
% 1.24/1.46 tff(2736,plain,
% 1.24/1.46 (b(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[63, 2735])).
% 1.24/1.46 tff(2737,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2738,plain,
% 1.24/1.46 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2739,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2738])).
% 1.24/1.46 tff(2740,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2739, 2737])).
% 1.24/1.46 tff(2741,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2742,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 1.24/1.46 tff(2743,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2742, 116, 270, 2189, 2736])).
% 1.24/1.46 tff(2744,plain,
% 1.24/1.46 (r(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[402, 21, 135, 2743])).
% 1.24/1.46 tff(2745,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2746,plain,
% 1.24/1.46 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2747,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2746])).
% 1.24/1.46 tff(2748,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2747, 2745])).
% 1.24/1.46 tff(2749,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2750,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 1.24/1.46 tff(2751,plain,
% 1.24/1.46 (~r(elem!1, s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2750, 77, 620, 2744])).
% 1.24/1.46 tff(2752,plain,
% 1.24/1.46 (b(elem!1, s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1345, 2751, 1620])).
% 1.24/1.46 tff(2753,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2754,plain,
% 1.24/1.47 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2755,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2754])).
% 1.24/1.47 tff(2756,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2755, 2753])).
% 1.24/1.47 tff(2757,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2758,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 1.24/1.47 tff(2759,plain,
% 1.24/1.47 (~r(s(s(s(z))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2758, 77, 575, 620, 2744])).
% 1.24/1.47 tff(2760,plain,
% 1.24/1.47 (b(s(s(s(z))), elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2725, 2759, 2688])).
% 1.24/1.47 tff(2761,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2762,plain,
% 1.24/1.47 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2763,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2762])).
% 1.24/1.47 tff(2764,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2763, 2761])).
% 1.24/1.47 tff(2765,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2766,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 1.24/1.47 tff(2767,plain,
% 1.24/1.47 ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2766, 116])).
% 1.24/1.47 tff(2768,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2767, 2760, 2752, 1055, 2736])).
% 1.24/1.47 tff(2769,plain,((~r(elem!1, s(z))) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(2770,plain,
% 1.24/1.47 (~r(elem!1, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2769, 2683, 2623, 2687, 2408, 2625, 1303, 422])).
% 1.24/1.47 tff(2771,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2772,plain,
% 1.24/1.47 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2773,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2772])).
% 1.24/1.47 tff(2774,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2773, 2771])).
% 1.24/1.47 tff(2775,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2776,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 1.24/1.47 tff(2777,plain,
% 1.24/1.47 (~r(z, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2776, 77, 2675, 156])).
% 1.24/1.47 tff(2778,plain,
% 1.24/1.47 (b(z, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[289, 2777])).
% 1.24/1.47 tff(2779,plain,
% 1.24/1.47 (~b(elem!1, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1298, 2683, 2625, 2778])).
% 1.24/1.47 tff(2780,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[633, 2779, 2770, 2685])).
% 1.24/1.47 tff(2781,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1) | b(elem!1, z) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | r(z, elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(2782,plain,
% 1.24/1.47 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2781, 1362, 422, 1455, 156, 28, 2247, 1303, 1331, 1052, 340])).
% 1.24/1.47 tff(2783,plain,
% 1.24/1.47 (r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[149, 2782])).
% 1.24/1.47 tff(2784,plain,
% 1.24/1.47 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[336, 2783, 156])).
% 1.24/1.47 tff(2785,plain,
% 1.24/1.47 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[325, 2784])).
% 1.24/1.47 tff(2786,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2787,plain,
% 1.24/1.47 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(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)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2788,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2787])).
% 1.24/1.47 tff(2789,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2788, 2786])).
% 1.24/1.47 tff(2790,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2791,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 1.24/1.47 tff(2792,plain,
% 1.24/1.47 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2791, 116, 2247, 1303, 2442])).
% 1.24/1.47 tff(2793,plain,
% 1.24/1.47 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[89, 21, 2792, 56])).
% 1.24/1.47 tff(2794,plain,
% 1.24/1.47 (~r(s(z), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2515, 77, 2793, 156])).
% 1.24/1.47 tff(2795,plain,
% 1.24/1.47 (b(s(z), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[194, 2794])).
% 1.24/1.47 tff(2796,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2797,plain,
% 1.24/1.47 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2798,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2797])).
% 1.24/1.47 tff(2799,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2798, 2796])).
% 1.24/1.47 tff(2800,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2801,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2800, 2799])).
% 1.24/1.47 tff(2802,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2801, 116, 2247, 28, 2442, 2795, 249])).
% 1.24/1.47 tff(2803,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(2804,plain,
% 1.24/1.47 (~b(z, s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2803, 2785, 28, 2247, 156, 1303])).
% 1.24/1.47 tff(2805,plain,
% 1.24/1.47 (r(z, s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1174, 2804])).
% 1.24/1.47 tff(2806,plain,
% 1.24/1.47 (r(elem!1, z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[545, 439, 1455])).
% 1.24/1.47 tff(2807,plain,
% 1.24/1.47 (~(s(s(s(z))) = elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1620, 2686])).
% 1.24/1.47 tff(2808,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2809,plain,
% 1.24/1.47 (((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2810,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2809])).
% 1.24/1.47 tff(2811,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2810, 2808])).
% 1.24/1.47 tff(2812,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2813,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 1.24/1.47 tff(2814,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2813, 77, 575, 360, 155])).
% 1.24/1.47 tff(2815,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(2816,plain,
% 1.24/1.47 (~r(s(z), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2815, 358, 575])).
% 1.24/1.47 tff(2817,plain,
% 1.24/1.47 (b(s(z), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[210, 2816])).
% 1.24/1.47 tff(2818,plain,
% 1.24/1.47 (~r(elem!1, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2769, 2817, 575, 2807, 1620, 1055, 1303, 422])).
% 1.24/1.47 tff(2819,plain,
% 1.24/1.47 (b(elem!1, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[633, 2818, 421])).
% 1.24/1.47 tff(2820,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2821,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2822,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2821, 2820])).
% 1.24/1.47 tff(2823,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2822, 116, 1055, 2817, 2819, 1303, 1331])).
% 1.24/1.47 tff(2824,plain,((s(z) = elem!1) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (s(s(z)) = elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(2825,plain,
% 1.24/1.47 (s(z) = elem!1),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2824, 1053, 1303, 1331, 2806, 2408, 422, 340])).
% 1.24/1.47 tff(2826,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2016, 2825, 28])).
% 1.24/1.47 tff(2827,plain,
% 1.24/1.47 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1476])).
% 1.24/1.47 tff(2828,plain,
% 1.24/1.47 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.24/1.47 inference(symmetry,[status(thm)],[2827])).
% 1.24/1.47 tff(2829,plain,
% 1.24/1.47 (b(s(s(elem!1)), z)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2247, 2828])).
% 1.24/1.47 tff(2830,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.24/1.47 tff(2831,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2830, 2829])).
% 1.24/1.47 tff(2832,plain,((~b(s(s(s(z))), z)) | b(s(s(elem!1)), z) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(2833,plain,
% 1.24/1.47 (b(s(s(elem!1)), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2832, 2825, 2247])).
% 1.24/1.47 tff(2834,plain,
% 1.24/1.47 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2825])).
% 1.24/1.47 tff(2835,plain,
% 1.24/1.47 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2834])).
% 1.24/1.47 tff(2836,plain,
% 1.24/1.47 (~r(elem!1, s(s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[314, 2835])).
% 1.24/1.47 tff(2837,plain,
% 1.24/1.47 (b(elem!1, s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1068, 2836, 1362])).
% 1.24/1.47 tff(2838,plain,
% 1.24/1.47 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2825])).
% 1.24/1.47 tff(2839,plain,
% 1.24/1.47 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2838])).
% 1.24/1.47 tff(2840,plain,
% 1.24/1.47 (~(s(s(elem!1)) = elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[566, 2839])).
% 1.24/1.47 tff(2841,plain,
% 1.24/1.47 (s(s(z)) = s(elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2825])).
% 1.24/1.47 tff(2842,plain,
% 1.24/1.47 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2841])).
% 1.24/1.47 tff(2843,plain,
% 1.24/1.47 (b(s(elem!1), z)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1303, 2842])).
% 1.24/1.47 tff(2844,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.24/1.47 tff(2845,plain,
% 1.24/1.47 (~(s(s(z)) = elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[480, 466])).
% 1.24/1.47 tff(2846,plain,
% 1.24/1.47 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1476, 1512])).
% 1.24/1.47 tff(2847,plain,
% 1.24/1.47 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(z)) = s(s(s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2846, 98])).
% 1.24/1.47 tff(2848,plain,
% 1.24/1.47 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[2847])).
% 1.24/1.47 tff(2849,plain,
% 1.24/1.47 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2848])).
% 1.24/1.47 tff(2850,plain,
% 1.24/1.47 (~(s(s(elem!1)) = s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[603, 2849])).
% 1.24/1.47 tff(2851,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2852,plain,
% 1.24/1.47 (((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(2853,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[2852])).
% 1.24/1.47 tff(2854,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[2853, 2851])).
% 1.24/1.47 tff(2855,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(2856,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[2855, 2854])).
% 1.24/1.47 tff(2857,plain,
% 1.24/1.47 (~b(s(s(elem!1)), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2856, 116, 1055, 1054, 573, 2844])).
% 1.24/1.47 tff(2858,plain,
% 1.24/1.47 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[765, 21, 2857])).
% 1.24/1.47 tff(2859,plain,
% 1.24/1.47 (r(s(s(elem!1)), s(elem!1))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2858, 2850])).
% 1.24/1.48 tff(2860,plain,
% 1.24/1.48 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1512])).
% 1.24/1.48 tff(2861,plain,
% 1.24/1.48 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.24/1.48 inference(symmetry,[status(thm)],[2860])).
% 1.24/1.48 tff(2862,plain,
% 1.24/1.48 (r(s(elem!1), elem!1)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[428, 2861])).
% 1.24/1.48 tff(2863,plain,
% 1.24/1.48 (~r(s(elem!1), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[758, 77, 752, 2609])).
% 1.24/1.48 tff(2864,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2863, 2862])).
% 1.24/1.48 tff(2865,plain,((~r(s(s(z)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2866,plain,
% 1.24/1.48 (~r(s(s(z)), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2865, 2859, 752, 466])).
% 1.24/1.48 tff(2867,plain,
% 1.24/1.48 (b(s(s(z)), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[426, 2866, 2845])).
% 1.24/1.48 tff(2868,plain,
% 1.24/1.48 (b(s(elem!1), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1549, 2867, 466])).
% 1.24/1.48 tff(2869,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2870,plain,
% 1.24/1.48 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2871,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2870])).
% 1.24/1.48 tff(2872,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[2871, 2869])).
% 1.24/1.48 tff(2873,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(2874,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2873, 2872])).
% 1.24/1.48 tff(2875,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2874, 116, 1055, 1054, 2868, 2844, 2023])).
% 1.24/1.48 tff(2876,plain,((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(z)) = s(s(s(z)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2877,plain,
% 1.24/1.48 ((~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2876, 100])).
% 1.24/1.48 tff(2878,plain,
% 1.24/1.48 (~r(s(s(elem!1)), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2877, 2837, 2833, 2825, 2826, 2843, 1053])).
% 1.24/1.48 tff(2879,plain,
% 1.24/1.48 (b(s(s(elem!1)), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[743, 2878, 2840])).
% 1.24/1.48 tff(2880,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2881,plain,
% 1.24/1.48 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2882,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2881])).
% 1.24/1.48 tff(2883,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[2882, 2880])).
% 1.24/1.48 tff(2884,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(2885,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2884, 2883])).
% 1.24/1.48 tff(2886,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2885, 116, 1053, 2879, 2837, 2833, 2826])).
% 1.24/1.48 tff(2887,plain,((elem!1 = z) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), z)) | r(s(z), s(s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (s(s(z)) = elem!1) | b(s(z), elem!1) | r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2888,plain,
% 1.24/1.48 (elem!1 = z),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2887, 1362, 1303, 2784, 2247, 28, 1331, 422, 340, 1052, 1455])).
% 1.24/1.48 tff(2889,plain,
% 1.24/1.48 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2888])).
% 1.24/1.48 tff(2890,plain,
% 1.24/1.48 ((~b(s(z), elem!1)) <=> (~b(s(z), z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2889])).
% 1.24/1.48 tff(2891,plain,
% 1.24/1.48 (~b(s(z), z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[340, 2890])).
% 1.24/1.48 tff(2892,plain,
% 1.24/1.48 (r(s(z), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[210, 2891])).
% 1.24/1.48 tff(2893,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2681, 77, 2892, 2805, 156])).
% 1.24/1.48 tff(2894,plain,((elem!1 = s(s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | b(s(z), elem!1) | (~b(s(s(z)), elem!1)) | (s(s(z)) = elem!1) | r(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2895,plain,
% 1.24/1.48 (elem!1 = s(s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2894, 2409, 28, 2247, 1303, 340, 156, 422, 1052, 1455])).
% 1.24/1.48 tff(2896,plain,
% 1.24/1.48 (~(s(z) = elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1531, 2895])).
% 1.24/1.48 tff(2897,plain,
% 1.24/1.48 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(2898,plain,
% 1.24/1.48 ((z = elem!1) <=> (z = s(s(s(s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2895])).
% 1.24/1.48 tff(2899,plain,
% 1.24/1.48 ((z = elem!1) <=> (s(s(s(s(z)))) = z)),
% 1.24/1.48 inference(transitivity,[status(thm)],[2898, 2897])).
% 1.24/1.48 tff(2900,plain,
% 1.24/1.48 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 1.24/1.48 inference(symmetry,[status(thm)],[2899])).
% 1.24/1.48 tff(2901,plain,
% 1.24/1.48 ((~(s(s(s(s(z)))) = z)) <=> (~(z = elem!1))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2900])).
% 1.24/1.48 tff(2902,plain,
% 1.24/1.48 (~(z = elem!1)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[242, 2901])).
% 1.24/1.48 tff(2903,plain,
% 1.24/1.48 (b(z, elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1044, 2902, 1052])).
% 1.24/1.48 tff(2904,plain,
% 1.24/1.48 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 1.24/1.48 inference(transitivity,[status(thm)],[2900, 441])).
% 1.24/1.48 tff(2905,plain,
% 1.24/1.48 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2904])).
% 1.24/1.48 tff(2906,plain,
% 1.24/1.48 (~(elem!1 = z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[242, 2905])).
% 1.24/1.48 tff(2907,plain,
% 1.24/1.48 (r(elem!1, z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[545, 2906, 1455])).
% 1.24/1.48 tff(2908,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2824, 2907, 2903, 1303, 2409, 2896, 2408, 422, 340])).
% 1.24/1.48 tff(2909,plain,((s(s(z)) = elem!1) | (~b(s(s(z)), z)) | b(s(z), elem!1) | b(elem!1, z) | r(z, elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2910,plain,
% 1.24/1.48 (r(z, elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2909, 2404, 340, 1455, 1303, 28, 2247, 156, 1674])).
% 1.24/1.48 tff(2911,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2912,plain,
% 1.24/1.48 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2913,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2912])).
% 1.24/1.48 tff(2914,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[2913, 2911])).
% 1.24/1.48 tff(2915,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(2916,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 1.24/1.48 tff(2917,plain,
% 1.24/1.48 (~r(z, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2916, 77, 448, 360])).
% 1.24/1.48 tff(2918,plain,
% 1.24/1.48 (b(z, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[289, 2917])).
% 1.24/1.48 tff(2919,plain,
% 1.24/1.48 (~r(s(z), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[690, 360, 448])).
% 1.24/1.48 tff(2920,plain,
% 1.24/1.48 (b(s(z), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[210, 2919])).
% 1.24/1.48 tff(2921,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2922,plain,
% 1.24/1.48 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2923,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2922])).
% 1.24/1.48 tff(2924,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[2923, 2921])).
% 1.24/1.48 tff(2925,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(2926,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 1.24/1.48 tff(2927,plain,
% 1.24/1.48 (~b(s(z), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2926, 116, 2920, 2918, 2247])).
% 1.24/1.48 tff(2928,plain,
% 1.24/1.48 (r(s(z), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[194, 2927])).
% 1.24/1.48 tff(2929,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2930,plain,
% 1.24/1.48 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2931,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2930])).
% 1.24/1.48 tff(2932,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[2931, 2929])).
% 1.24/1.48 tff(2933,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(2934,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2933, 2932])).
% 1.24/1.48 tff(2935,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2934, 116, 270, 271, 2247, 1303, 27])).
% 1.24/1.48 tff(2936,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2937,plain,
% 1.24/1.48 (~b(s(s(z)), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2936, 2918, 2247, 1303, 2920])).
% 1.24/1.48 tff(2938,plain,
% 1.24/1.48 (r(s(s(z)), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[105, 2937])).
% 1.24/1.48 tff(2939,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2317, 77, 2938, 2928, 156])).
% 1.24/1.48 tff(2940,plain,((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2941,plain,
% 1.24/1.48 (~r(s(z), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2940, 1303, 2247, 156, 2910])).
% 1.24/1.48 tff(2942,plain,
% 1.24/1.48 (s(z) = elem!1),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[357, 2941, 340])).
% 1.24/1.48 tff(2943,plain,
% 1.24/1.48 (s(s(z)) = s(elem!1)),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2942])).
% 1.24/1.48 tff(2944,plain,
% 1.24/1.48 (s(elem!1) = s(s(z))),
% 1.24/1.48 inference(symmetry,[status(thm)],[2943])).
% 1.24/1.48 tff(2945,plain,
% 1.24/1.48 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2944])).
% 1.24/1.48 tff(2946,plain,
% 1.24/1.48 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.24/1.48 inference(symmetry,[status(thm)],[2945])).
% 1.24/1.48 tff(2947,plain,
% 1.24/1.48 (r(s(z), z) <=> r(elem!1, z)),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2942])).
% 1.24/1.48 tff(2948,plain,
% 1.24/1.48 (~b(s(z), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1458, 2942, 1455])).
% 1.24/1.48 tff(2949,plain,
% 1.24/1.48 (r(s(z), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[210, 2948])).
% 1.24/1.48 tff(2950,plain,
% 1.24/1.48 (r(elem!1, z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2949, 2947])).
% 1.24/1.48 tff(2951,plain,
% 1.24/1.48 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1512])).
% 1.24/1.48 tff(2952,plain,
% 1.24/1.48 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.24/1.48 inference(symmetry,[status(thm)],[2951])).
% 1.24/1.48 tff(2953,plain,
% 1.24/1.48 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[466])).
% 1.24/1.48 tff(2954,plain,
% 1.24/1.48 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 1.24/1.48 inference(symmetry,[status(thm)],[2953])).
% 1.24/1.48 tff(2955,plain,
% 1.24/1.48 ((~r(elem!1, s(s(z)))) <=> (~r(s(z), s(s(z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2954])).
% 1.24/1.48 tff(2956,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 1.24/1.48 tff(2957,plain,
% 1.24/1.48 (~r(s(z), s(s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2956, 2955])).
% 1.24/1.48 tff(2958,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[156, 2957])).
% 1.24/1.48 tff(2959,plain,((~(s(z) = elem!1)) | (~r(s(z), s(s(z)))) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(2960,plain,
% 1.24/1.48 (r(elem!1, s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2959, 466, 156])).
% 1.24/1.48 tff(2961,plain,
% 1.24/1.48 (r(elem!1, s(elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2960, 2952])).
% 1.24/1.48 tff(2962,plain,
% 1.24/1.48 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1512])).
% 1.24/1.48 tff(2963,plain,
% 1.24/1.48 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.24/1.48 inference(symmetry,[status(thm)],[2962])).
% 1.24/1.48 tff(2964,plain,
% 1.24/1.48 (~b(z, s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2803, 249, 28, 2247, 156, 1303])).
% 1.24/1.48 tff(2965,plain,
% 1.24/1.48 (r(z, s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1174, 2964])).
% 1.24/1.48 tff(2966,plain,
% 1.24/1.48 (r(z, s(elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2965, 2963])).
% 1.24/1.48 tff(2967,plain,
% 1.24/1.48 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1475])).
% 1.24/1.48 tff(2968,plain,
% 1.24/1.48 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2967])).
% 1.24/1.48 tff(2969,plain,
% 1.24/1.48 (~b(z, s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2525, 249, 28, 2247, 156, 1303])).
% 1.24/1.48 tff(2970,plain,
% 1.24/1.48 (~b(z, s(s(elem!1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 1.24/1.48 tff(2971,plain,
% 1.24/1.48 (r(z, s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[514, 2970])).
% 1.24/1.48 tff(2972,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2973,plain,
% 1.24/1.48 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(2974,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[2973])).
% 1.24/1.48 tff(2975,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[2974, 2972])).
% 1.24/1.48 tff(2976,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(2977,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[2976, 2975])).
% 1.24/1.48 tff(2978,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2977, 77, 575, 2971, 2966, 2961])).
% 1.24/1.48 tff(2979,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(2980,plain,
% 1.24/1.49 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2979, 2950, 2942, 28, 2247, 156, 1303])).
% 1.24/1.49 tff(2981,plain,
% 1.24/1.49 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[325, 2980])).
% 1.24/1.49 tff(2982,plain,
% 1.24/1.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[336, 2981, 156])).
% 1.24/1.49 tff(2983,plain,
% 1.24/1.49 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[149, 2982])).
% 1.24/1.49 tff(2984,plain,
% 1.24/1.49 (~(elem!1 = s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1531, 2942])).
% 1.24/1.49 tff(2985,plain,
% 1.24/1.49 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[2942])).
% 1.24/1.49 tff(2986,plain,
% 1.24/1.49 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[2985])).
% 1.24/1.49 tff(2987,plain,
% 1.24/1.49 (~b(elem!1, s(s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[2980, 2986])).
% 1.24/1.49 tff(2988,plain,
% 1.24/1.49 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1068, 2987, 2984])).
% 1.24/1.49 tff(2989,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2671, 2988, 2950])).
% 1.24/1.49 tff(2990,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[247, 2989])).
% 1.24/1.49 tff(2991,plain,
% 1.24/1.49 (~b(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2450, 2990, 28, 2247, 2983])).
% 1.24/1.49 tff(2992,plain,
% 1.24/1.49 (r(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1174, 2991])).
% 1.24/1.49 tff(2993,plain,
% 1.24/1.49 (r(z, s(elem!1))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[2992, 2946])).
% 1.24/1.49 tff(2994,plain,
% 1.24/1.49 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[2944])).
% 1.24/1.49 tff(2995,plain,
% 1.24/1.49 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[2994])).
% 1.24/1.49 tff(2996,plain,
% 1.24/1.49 (r(elem!1, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2959, 2942, 156])).
% 1.24/1.49 tff(2997,plain,
% 1.24/1.49 (r(elem!1, s(elem!1))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[2996, 2995])).
% 1.24/1.49 tff(2998,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(2999,plain,
% 1.24/1.49 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3000,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[2999])).
% 1.24/1.49 tff(3001,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3000, 2998])).
% 1.24/1.49 tff(3002,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3003,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 1.24/1.49 tff(3004,plain,
% 1.24/1.49 ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3003, 77, 2910, 2988])).
% 1.24/1.49 tff(3005,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3004, 2997, 2993])).
% 1.24/1.49 tff(3006,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | b(elem!1, z) | b(s(z), elem!1) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3007,plain,
% 1.24/1.49 (~b(s(s(z)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3006, 156, 2247, 28, 1455, 340, 1674])).
% 1.24/1.49 tff(3008,plain,
% 1.24/1.49 (~(elem!1 = z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1680, 1331, 2])).
% 1.24/1.49 tff(3009,plain,
% 1.24/1.49 (r(elem!1, z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[545, 3008, 1455])).
% 1.24/1.49 tff(3010,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3011,plain,
% 1.24/1.49 (((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3012,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3011])).
% 1.24/1.49 tff(3013,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3012, 3010])).
% 1.24/1.49 tff(3014,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3015,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 1.24/1.49 tff(3016,plain,
% 1.24/1.49 (~r(elem!1, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3015, 77, 3009, 26])).
% 1.24/1.49 tff(3017,plain,
% 1.24/1.49 (~(s(z) = elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2959, 3016, 156])).
% 1.24/1.49 tff(3018,plain,
% 1.24/1.49 (r(s(z), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[357, 3017, 340])).
% 1.24/1.49 tff(3019,plain,
% 1.24/1.49 (~(z = elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[445, 3008])).
% 1.24/1.49 tff(3020,plain,
% 1.24/1.49 (~(elem!1 = s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[420, 3017])).
% 1.24/1.49 tff(3021,plain,
% 1.24/1.49 (~r(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2815, 360, 575])).
% 1.24/1.49 tff(3022,plain,
% 1.24/1.49 (b(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[210, 3021])).
% 1.24/1.49 tff(3023,plain,
% 1.24/1.49 (~b(s(s(s(z))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2742, 116, 270, 271, 2247])).
% 1.24/1.49 tff(3024,plain,
% 1.24/1.49 (r(s(s(s(z))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[402, 21, 135, 3023])).
% 1.24/1.49 tff(3025,plain,
% 1.24/1.49 (~b(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1298, 271, 1055, 270])).
% 1.24/1.49 tff(3026,plain,
% 1.24/1.49 (r(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[633, 3025, 1046])).
% 1.24/1.49 tff(3027,plain,
% 1.24/1.49 (~r(elem!1, s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2750, 77, 3026, 3024])).
% 1.24/1.49 tff(3028,plain,
% 1.24/1.49 (b(elem!1, s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1345, 3027, 1620])).
% 1.24/1.49 tff(3029,plain,
% 1.24/1.49 (~r(s(s(s(z))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2758, 77, 575, 3026, 3024])).
% 1.24/1.49 tff(3030,plain,
% 1.24/1.49 (b(s(s(s(z))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2725, 3029, 2807])).
% 1.24/1.49 tff(3031,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2767, 3030, 3028, 2247, 1055])).
% 1.24/1.49 tff(3032,plain,((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z)) | (~b(s(z), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3033,plain,
% 1.24/1.49 (~b(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3032, 1055, 2247, 1620, 575, 3022, 1046])).
% 1.24/1.49 tff(3034,plain,
% 1.24/1.49 (r(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[289, 3033])).
% 1.24/1.49 tff(3035,plain,
% 1.24/1.49 (~r(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2095, 3034, 575])).
% 1.24/1.49 tff(3036,plain,
% 1.24/1.49 (b(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[633, 3035, 1046])).
% 1.24/1.49 tff(3037,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3038,plain,
% 1.24/1.49 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3039,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3038])).
% 1.24/1.49 tff(3040,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3039, 3037])).
% 1.24/1.49 tff(3041,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3042,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3041, 3040])).
% 1.24/1.49 tff(3043,plain,
% 1.24/1.49 (~b(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3042, 116, 1055, 3022, 3036, 1331])).
% 1.24/1.49 tff(3044,plain,
% 1.24/1.49 (r(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1174, 3043])).
% 1.24/1.49 tff(3045,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3046,plain,
% 1.24/1.49 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, s(z)))) <=> ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3047,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3046])).
% 1.24/1.49 tff(3048,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3047, 3045])).
% 1.24/1.49 tff(3049,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3050,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3049, 3048])).
% 1.24/1.49 tff(3051,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3050, 77, 360, 3034, 3044, 156])).
% 1.24/1.49 tff(3052,plain,((~b(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (elem!1 = s(z)) | (~r(elem!1, z)) | (~b(s(s(s(z))), z)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3053,plain,
% 1.24/1.49 (~b(z, elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3052, 3018, 156, 1331, 3020, 3009, 2247, 2408])).
% 1.24/1.49 tff(3054,plain,
% 1.24/1.49 (r(z, elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1044, 3053, 3019])).
% 1.24/1.49 tff(3055,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3056,plain,
% 1.24/1.49 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3057,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3056])).
% 1.24/1.49 tff(3058,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3057, 3055])).
% 1.24/1.49 tff(3059,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3060,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3059, 3058])).
% 1.24/1.49 tff(3061,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3060, 77, 575, 360, 359, 2928])).
% 1.24/1.49 tff(3062,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3063,plain,
% 1.24/1.49 (~r(elem!1, s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3062, 3054, 3018, 2247, 3009])).
% 1.24/1.49 tff(3064,plain,
% 1.24/1.49 (b(elem!1, s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1345, 3063, 2408])).
% 1.24/1.49 tff(3065,plain,
% 1.24/1.49 (~r(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2916, 77, 3054, 3018])).
% 1.24/1.49 tff(3066,plain,
% 1.24/1.49 (b(z, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[289, 3065])).
% 1.24/1.49 tff(3067,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3068,plain,
% 1.24/1.49 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3069,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3068])).
% 1.24/1.49 tff(3070,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3069, 3067])).
% 1.24/1.49 tff(3071,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3072,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 1.24/1.49 tff(3073,plain,
% 1.24/1.49 (~b(elem!1, s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3072, 116, 3066, 2247, 3064, 28])).
% 1.24/1.49 tff(3074,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3075,plain,
% 1.24/1.49 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3076,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3075])).
% 1.24/1.49 tff(3077,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3076, 3074])).
% 1.24/1.49 tff(3078,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3079,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 1.24/1.49 tff(3080,plain,
% 1.24/1.49 (~b(s(s(s(s(z)))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3079, 116, 3066, 2247, 3064, 28])).
% 1.24/1.49 tff(3081,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.49 tff(3082,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1596, 2416, 3081])).
% 1.24/1.49 tff(3083,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3084,plain,
% 1.24/1.49 (((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3085,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3084])).
% 1.24/1.49 tff(3086,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.50 inference(transitivity,[status(thm)],[3085, 3083])).
% 1.24/1.50 tff(3087,plain,
% 1.24/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(3088,plain,
% 1.24/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 1.24/1.50 tff(3089,plain,
% 1.24/1.50 (~r(z, s(s(s(s(z)))))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[3088, 77, 448, 3082])).
% 1.24/1.50 tff(3090,plain,
% 1.24/1.50 (r(elem!1, s(s(s(s(z)))))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[1068, 1362, 1525])).
% 1.24/1.50 tff(3091,plain,
% 1.24/1.50 (~r(s(s(s(s(z)))), z)),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[2671, 3090, 575])).
% 1.24/1.50 tff(3092,plain,
% 1.24/1.50 (b(s(s(s(s(z)))), z)),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[247, 3091])).
% 1.24/1.50 tff(3093,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(3094,plain,
% 1.24/1.50 (((~b(s(s(s(s(z)))), 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(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(3095,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[3094])).
% 1.24/1.50 tff(3096,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.50 inference(transitivity,[status(thm)],[3095, 3093])).
% 1.24/1.50 tff(3097,plain,
% 1.24/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z))))))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(3098,plain,
% 1.24/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[3097, 3096])).
% 1.24/1.50 tff(3099,plain,
% 1.24/1.50 ($false),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[3098, 116, 2247, 28, 254, 1176])).
% 1.24/1.50 tff(3100,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(3101,plain,
% 1.34/1.50 (~b(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3100, 3092, 28, 2247])).
% 1.34/1.50 tff(3102,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1576, 21, 3101, 3089, 1563])).
% 1.34/1.50 tff(3103,plain,((elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(elem!1, z)) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(3104,plain,
% 1.34/1.50 (elem!1 = s(s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3103, 3054, 28, 2247, 3009, 3080, 3073])).
% 1.34/1.50 tff(3105,plain,
% 1.34/1.50 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3104])).
% 1.34/1.50 tff(3106,plain,
% 1.34/1.50 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1331, 3105])).
% 1.34/1.50 tff(3107,plain,
% 1.34/1.50 (~r(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2815, 3018, 3009])).
% 1.34/1.50 tff(3108,plain,
% 1.34/1.50 (b(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[210, 3107])).
% 1.34/1.50 tff(3109,plain,
% 1.34/1.50 (~b(s(z), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2926, 116, 3108, 3066, 2247])).
% 1.34/1.50 tff(3110,plain,
% 1.34/1.50 (r(s(z), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[194, 3109])).
% 1.34/1.50 tff(3111,plain,
% 1.34/1.50 (~r(s(s(z)), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2319, 3110, 156])).
% 1.34/1.50 tff(3112,plain,
% 1.34/1.50 (b(s(s(z)), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[105, 3111])).
% 1.34/1.50 tff(3113,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3114,plain,
% 1.34/1.50 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3115,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3114])).
% 1.34/1.50 tff(3116,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3115, 3113])).
% 1.34/1.50 tff(3117,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(3118,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3117, 3116])).
% 1.34/1.50 tff(3119,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3118, 116, 3066, 2247, 3112, 3106, 28])).
% 1.34/1.50 tff(3120,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | b(s(z), elem!1) | b(elem!1, z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(3121,plain,
% 1.34/1.50 (~b(s(s(z)), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3120, 156, 28, 2247, 340, 1455, 3007])).
% 1.34/1.50 tff(3122,plain,
% 1.34/1.50 (s(s(z)) = elem!1),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[426, 3121, 1674])).
% 1.34/1.50 tff(3123,plain,
% 1.34/1.50 (~(s(z) = elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[480, 3122])).
% 1.34/1.50 tff(3124,plain,
% 1.34/1.50 (r(s(z), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[357, 3123, 340])).
% 1.34/1.50 tff(3125,plain,
% 1.34/1.50 (s(s(s(z))) = s(elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3122])).
% 1.34/1.50 tff(3126,plain,
% 1.34/1.50 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3125])).
% 1.34/1.50 tff(3127,plain,
% 1.34/1.50 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[3126])).
% 1.34/1.50 tff(3128,plain,
% 1.34/1.50 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3127])).
% 1.34/1.50 tff(3129,plain,
% 1.34/1.50 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3128, 1580])).
% 1.34/1.50 tff(3130,plain,
% 1.34/1.50 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.50 inference(symmetry,[status(thm)],[3129])).
% 1.34/1.50 tff(3131,plain,
% 1.34/1.50 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3130])).
% 1.34/1.50 tff(3132,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3122])).
% 1.34/1.50 tff(3133,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3132, 1580])).
% 1.34/1.50 tff(3134,plain,
% 1.34/1.50 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3133])).
% 1.34/1.50 tff(3135,plain,
% 1.34/1.50 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[137, 3134])).
% 1.34/1.50 tff(3136,plain,
% 1.34/1.50 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3135, 3131])).
% 1.34/1.50 tff(3137,plain,
% 1.34/1.50 (s(elem!1) = s(s(s(z)))),
% 1.34/1.50 inference(symmetry,[status(thm)],[3125])).
% 1.34/1.50 tff(3138,plain,
% 1.34/1.50 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3137])).
% 1.34/1.50 tff(3139,plain,
% 1.34/1.50 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.34/1.50 inference(symmetry,[status(thm)],[3138])).
% 1.34/1.50 tff(3140,plain,
% 1.34/1.50 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3122])).
% 1.34/1.50 tff(3141,plain,
% 1.34/1.50 (r(s(s(z)), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[25, 3007])).
% 1.34/1.50 tff(3142,plain,
% 1.34/1.50 (r(elem!1, z)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3141, 3140])).
% 1.34/1.50 tff(3143,plain,
% 1.34/1.50 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3122])).
% 1.34/1.50 tff(3144,plain,
% 1.34/1.50 ((s(s(z)) = z) <=> (z = elem!1)),
% 1.34/1.50 inference(transitivity,[status(thm)],[3143, 440])).
% 1.34/1.50 tff(3145,plain,
% 1.34/1.50 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3144])).
% 1.34/1.50 tff(3146,plain,
% 1.34/1.50 (~(z = elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[11, 3145])).
% 1.34/1.50 tff(3147,plain,
% 1.34/1.50 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[557])).
% 1.34/1.50 tff(3148,plain,
% 1.34/1.50 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3147, 1580])).
% 1.34/1.50 tff(3149,plain,
% 1.34/1.50 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.50 inference(symmetry,[status(thm)],[3148])).
% 1.34/1.50 tff(3150,plain,
% 1.34/1.50 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3149, 1093])).
% 1.34/1.50 tff(3151,plain,
% 1.34/1.50 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3150])).
% 1.34/1.50 tff(3152,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[370])).
% 1.34/1.50 tff(3153,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3152, 1580])).
% 1.34/1.50 tff(3154,plain,
% 1.34/1.50 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3153])).
% 1.34/1.50 tff(3155,plain,
% 1.34/1.50 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[137, 3154])).
% 1.34/1.50 tff(3156,plain,
% 1.34/1.50 (~(elem!1 = s(s(elem!1)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3155, 3151])).
% 1.34/1.50 tff(3157,plain,
% 1.34/1.50 (~(elem!1 = s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[420, 481])).
% 1.34/1.50 tff(3158,plain,
% 1.34/1.50 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[370])).
% 1.34/1.50 tff(3159,plain,
% 1.34/1.50 (r(elem!1, z)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[66, 3158])).
% 1.34/1.50 tff(3160,plain,
% 1.34/1.50 (~r(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2815, 3159, 360])).
% 1.34/1.50 tff(3161,plain,
% 1.34/1.50 (b(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[210, 3160])).
% 1.34/1.50 tff(3162,plain,
% 1.34/1.50 (~b(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3032, 1055, 2247, 1620, 3159, 3161, 3157])).
% 1.34/1.50 tff(3163,plain,
% 1.34/1.50 (r(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[289, 3162])).
% 1.34/1.50 tff(3164,plain,
% 1.34/1.50 (~r(elem!1, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2095, 3163, 3159])).
% 1.34/1.50 tff(3165,plain,
% 1.34/1.50 (b(elem!1, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[633, 3164, 3157])).
% 1.34/1.50 tff(3166,plain,
% 1.34/1.50 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3149])).
% 1.34/1.50 tff(3167,plain,
% 1.34/1.50 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3155, 3166])).
% 1.34/1.50 tff(3168,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3169,plain,
% 1.34/1.50 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3170,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3169])).
% 1.34/1.50 tff(3171,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3170, 3168])).
% 1.34/1.50 tff(3172,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(3173,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3172, 3171])).
% 1.34/1.50 tff(3174,plain,
% 1.34/1.50 (~b(z, s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3173, 116, 1055, 616, 270, 667])).
% 1.34/1.50 tff(3175,plain,
% 1.34/1.50 (r(z, s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[514, 3174])).
% 1.34/1.50 tff(3176,plain,
% 1.34/1.50 (~b(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1298, 667, 270, 1055])).
% 1.34/1.50 tff(3177,plain,
% 1.34/1.50 (r(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[289, 3176])).
% 1.34/1.50 tff(3178,plain,
% 1.34/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3179,plain,
% 1.34/1.50 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3180,plain,
% 1.34/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3179])).
% 1.34/1.50 tff(3181,plain,
% 1.34/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3180, 3178])).
% 1.34/1.50 tff(3182,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(3183,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3182, 3181])).
% 1.34/1.50 tff(3184,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3183, 77, 794, 494, 293])).
% 1.34/1.50 tff(3185,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(3186,plain,
% 1.34/1.50 (~r(s(s(elem!1)), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3185, 3177, 3175])).
% 1.34/1.50 tff(3187,plain,
% 1.34/1.50 (b(s(s(elem!1)), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[808, 3186])).
% 1.34/1.50 tff(3188,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3189,plain,
% 1.34/1.50 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3190,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3189])).
% 1.34/1.50 tff(3191,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[3190, 3188])).
% 1.34/1.50 tff(3192,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(3193,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[3192, 3191])).
% 1.34/1.50 tff(3194,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3193, 116, 1055, 3187, 616, 270, 667])).
% 1.34/1.50 tff(3195,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(3196,plain,
% 1.34/1.50 (~b(s(s(elem!1)), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[3195, 3165, 1055, 3161])).
% 1.34/1.50 tff(3197,plain,
% 1.34/1.50 (r(s(s(elem!1)), elem!1)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[743, 3196, 3167])).
% 1.34/1.50 tff(3198,plain,
% 1.34/1.50 (~r(s(s(elem!1)), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1245, 3197, 360])).
% 1.34/1.50 tff(3199,plain,
% 1.34/1.50 (b(s(s(elem!1)), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[808, 3198])).
% 1.34/1.50 tff(3200,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3201,plain,
% 1.34/1.50 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(3202,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[3201])).
% 1.34/1.50 tff(3203,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3202, 3200])).
% 1.34/1.51 tff(3204,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(3205,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.34/1.51 tff(3206,plain,
% 1.34/1.51 (~b(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3205, 116, 1055, 3199, 3161, 3165])).
% 1.34/1.51 tff(3207,plain,
% 1.34/1.51 (r(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1892, 3206, 3156])).
% 1.34/1.51 tff(3208,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.34/1.51 tff(3209,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3210,plain,
% 1.34/1.51 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3211,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3210])).
% 1.34/1.51 tff(3212,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3211, 3209])).
% 1.34/1.51 tff(3213,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(3214,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3213, 3212])).
% 1.34/1.51 tff(3215,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3214, 77, 575, 752, 3208])).
% 1.34/1.51 tff(3216,plain,((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3217,plain,
% 1.34/1.51 (~r(s(s(elem!1)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3216, 3197, 3159])).
% 1.34/1.51 tff(3218,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1426, 21, 508, 2830, 1480])).
% 1.34/1.51 tff(3219,plain,(r(s(s(elem!1)), z) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3220,plain,
% 1.34/1.51 (b(s(s(elem!1)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3219, 3217])).
% 1.34/1.51 tff(3221,plain,
% 1.34/1.51 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[370])).
% 1.34/1.51 tff(3222,plain,
% 1.34/1.51 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[576])).
% 1.34/1.51 tff(3223,plain,
% 1.34/1.51 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3222])).
% 1.34/1.51 tff(3224,plain,
% 1.34/1.51 (b(s(elem!1), z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2247, 635])).
% 1.34/1.51 tff(3225,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3226,plain,
% 1.34/1.51 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3227,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3226])).
% 1.34/1.51 tff(3228,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3227, 3225])).
% 1.34/1.51 tff(3229,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(3230,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 1.34/1.51 tff(3231,plain,
% 1.34/1.51 (~b(s(z), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3230, 116, 1055, 3161, 3165, 3224])).
% 1.34/1.51 tff(3232,plain,
% 1.34/1.51 (~b(s(z), s(s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3231, 3223])).
% 1.34/1.51 tff(3233,plain,
% 1.34/1.51 (r(s(z), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[194, 3232])).
% 1.34/1.51 tff(3234,plain,
% 1.34/1.51 (~r(s(s(z)), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2319, 3233, 156])).
% 1.34/1.51 tff(3235,plain,
% 1.34/1.51 (b(s(s(z)), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[105, 3234])).
% 1.34/1.51 tff(3236,plain,
% 1.34/1.51 (b(elem!1, s(s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3235, 3221])).
% 1.34/1.51 tff(3237,plain,
% 1.34/1.51 (~b(s(s(s(z))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2767, 3236, 2247, 1055])).
% 1.34/1.51 tff(3238,plain,
% 1.34/1.51 (r(s(s(s(z))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2725, 3237, 2807])).
% 1.34/1.51 tff(3239,plain,
% 1.34/1.51 (r(s(elem!1), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[647, 3238, 370])).
% 1.34/1.51 tff(3240,plain,
% 1.34/1.51 (~b(z, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[776, 3239, 370, 66, 3197, 3220])).
% 1.34/1.51 tff(3241,plain,
% 1.34/1.51 (r(z, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[514, 3240])).
% 1.34/1.51 tff(3242,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2205, 77, 3159, 3241, 3207])).
% 1.34/1.51 tff(3243,plain,((~b(z, elem!1)) | (~(s(s(z)) = elem!1)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3244,plain,
% 1.34/1.51 (~b(z, elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3243, 3122, 3141, 2247, 156, 3124, 2408])).
% 1.34/1.51 tff(3245,plain,
% 1.34/1.51 (r(z, elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1044, 3244, 3146])).
% 1.34/1.51 tff(3246,plain,
% 1.34/1.51 (~r(elem!1, s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3062, 3245, 3124, 2247, 3142])).
% 1.34/1.51 tff(3247,plain,
% 1.34/1.51 (b(elem!1, s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1345, 3246, 2408])).
% 1.34/1.51 tff(3248,plain,
% 1.34/1.51 (b(elem!1, s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3247, 3139])).
% 1.34/1.51 tff(3249,plain,
% 1.34/1.51 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3125])).
% 1.34/1.51 tff(3250,plain,
% 1.34/1.51 (b(s(elem!1), z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2247, 3249])).
% 1.34/1.51 tff(3251,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[557])).
% 1.34/1.51 tff(3252,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.51 inference(symmetry,[status(thm)],[3251])).
% 1.34/1.51 tff(3253,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[555])).
% 1.34/1.51 tff(3254,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3253, 3252])).
% 1.34/1.51 tff(3255,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[28, 3254])).
% 1.34/1.51 tff(3256,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[762, 3255])).
% 1.34/1.51 tff(3257,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(elem!1)), s(elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3258,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3257, 3122, 28])).
% 1.34/1.51 tff(3259,plain,
% 1.34/1.51 (~r(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2916, 77, 3245, 3124])).
% 1.34/1.51 tff(3260,plain,
% 1.34/1.51 (b(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[289, 3259])).
% 1.34/1.51 tff(3261,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3262,plain,
% 1.34/1.51 (((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3263,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3262])).
% 1.34/1.51 tff(3264,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3263, 3261])).
% 1.34/1.51 tff(3265,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(3266,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3265, 3264])).
% 1.34/1.51 tff(3267,plain,
% 1.34/1.51 (~b(s(s(elem!1)), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3266, 116, 3260, 3258, 3250, 3248])).
% 1.34/1.51 tff(3268,plain,
% 1.34/1.51 (r(s(s(elem!1)), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[743, 3267, 3136])).
% 1.34/1.51 tff(3269,plain,
% 1.34/1.51 (~r(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1245, 3268, 3124])).
% 1.34/1.51 tff(3270,plain,
% 1.34/1.51 (~r(s(z), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2815, 3142, 3124])).
% 1.34/1.51 tff(3271,plain,
% 1.34/1.51 (b(s(z), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[210, 3270])).
% 1.34/1.51 tff(3272,plain,
% 1.34/1.51 (~b(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1443, 3268, 3245, 3271])).
% 1.34/1.51 tff(3273,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[808, 3272, 3269])).
% 1.34/1.51 tff(3274,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(z)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3275,plain,
% 1.34/1.51 (b(elem!1, z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3274, 156, 28, 2234, 340, 1673])).
% 1.34/1.51 tff(3276,plain,
% 1.34/1.51 (~(s(s(z)) = elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[540, 3275, 2])).
% 1.34/1.51 tff(3277,plain,
% 1.34/1.51 (b(s(s(z)), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[426, 3276, 1673])).
% 1.34/1.51 tff(3278,plain,
% 1.34/1.51 (~r(s(s(z)), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2393, 2247, 28, 66])).
% 1.34/1.51 tff(3279,plain,
% 1.34/1.51 (b(s(s(z)), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[105, 3278])).
% 1.34/1.51 tff(3280,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3281,plain,
% 1.34/1.51 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3282,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3281])).
% 1.34/1.51 tff(3283,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3282, 3280])).
% 1.34/1.51 tff(3284,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(3285,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 1.34/1.51 tff(3286,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3285, 77, 448, 228, 2418])).
% 1.34/1.51 tff(3287,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3288,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3287, 228, 448])).
% 1.34/1.51 tff(3289,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.34/1.51 tff(3290,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2926, 116, 270, 271, 2247, 175])).
% 1.34/1.51 tff(3291,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3292,plain,
% 1.34/1.51 (~b(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3291, 175, 2247, 270])).
% 1.34/1.51 tff(3293,plain,
% 1.34/1.51 (r(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[289, 3292])).
% 1.34/1.51 tff(3294,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2916, 77, 448, 360, 293])).
% 1.34/1.51 tff(3295,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3296,plain,
% 1.34/1.51 (~r(s(z), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3295, 3293, 448])).
% 1.34/1.51 tff(3297,plain,
% 1.34/1.51 (s(z) = elem!1),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[357, 3296, 340])).
% 1.34/1.51 tff(3298,plain,
% 1.34/1.51 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1531, 3297])).
% 1.34/1.51 tff(3299,plain,
% 1.34/1.51 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1584, 3298])).
% 1.34/1.51 tff(3300,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1596, 3299, 3289])).
% 1.34/1.51 tff(3301,plain,
% 1.34/1.51 (s(s(z)) = s(elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3297])).
% 1.34/1.51 tff(3302,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3301])).
% 1.34/1.51 tff(3303,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[212, 3302])).
% 1.34/1.51 tff(3304,plain,
% 1.34/1.51 (b(s(s(elem!1)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2832, 3297, 2247])).
% 1.34/1.51 tff(3305,plain,
% 1.34/1.51 (b(s(elem!1), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1549, 3297, 1331])).
% 1.34/1.51 tff(3306,plain,
% 1.34/1.51 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3301])).
% 1.34/1.51 tff(3307,plain,
% 1.34/1.51 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3306])).
% 1.34/1.51 tff(3308,plain,
% 1.34/1.51 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3297])).
% 1.34/1.51 tff(3309,plain,
% 1.34/1.51 (b(elem!1, s(s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[175, 3308])).
% 1.34/1.51 tff(3310,plain,
% 1.34/1.51 (b(elem!1, s(s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3309, 3307])).
% 1.34/1.51 tff(3311,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3312,plain,
% 1.34/1.51 (((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3313,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3312])).
% 1.34/1.51 tff(3314,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3313, 3311])).
% 1.34/1.51 tff(3315,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(3316,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 1.34/1.51 tff(3317,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3316, 116, 3310, 3305, 3304, 3303, 3300])).
% 1.34/1.51 tff(3318,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | b(s(z), elem!1) | (~r(z, elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3319,plain,
% 1.34/1.51 (~b(s(z), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3318, 2266, 3288, 1331, 2247, 340, 448, 270])).
% 1.34/1.51 tff(3320,plain,
% 1.34/1.51 (r(s(z), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[194, 3319])).
% 1.34/1.51 tff(3321,plain,
% 1.34/1.51 (~r(s(z), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3295, 293, 448])).
% 1.34/1.51 tff(3322,plain,
% 1.34/1.51 (s(z) = elem!1),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[357, 3321, 340])).
% 1.34/1.51 tff(3323,plain,
% 1.34/1.51 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1531, 3322])).
% 1.34/1.51 tff(3324,plain,
% 1.34/1.51 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1584, 3323])).
% 1.34/1.51 tff(3325,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1596, 3324, 3289])).
% 1.34/1.51 tff(3326,plain,
% 1.34/1.51 (s(s(z)) = s(elem!1)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3322])).
% 1.34/1.51 tff(3327,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3326])).
% 1.34/1.51 tff(3328,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[212, 3327])).
% 1.34/1.51 tff(3329,plain,
% 1.34/1.51 (b(s(elem!1), elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1549, 3322, 1331])).
% 1.34/1.51 tff(3330,plain,
% 1.34/1.51 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3326])).
% 1.34/1.51 tff(3331,plain,
% 1.34/1.51 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3330])).
% 1.34/1.51 tff(3332,plain,
% 1.34/1.51 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3331])).
% 1.34/1.51 tff(3333,plain,
% 1.34/1.51 (~r(z, s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[301, 293, 292])).
% 1.34/1.51 tff(3334,plain,
% 1.34/1.51 (~r(z, s(s(elem!1)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3333, 3332])).
% 1.34/1.51 tff(3335,plain,
% 1.34/1.51 (b(z, s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[514, 3334])).
% 1.34/1.51 tff(3336,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3337,plain,
% 1.34/1.51 (((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3338,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[3337])).
% 1.34/1.51 tff(3339,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[3338, 3336])).
% 1.34/1.51 tff(3340,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(3341,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 1.34/1.51 tff(3342,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3341, 116, 537, 3335, 3329, 3328, 3325])).
% 1.34/1.51 tff(3343,plain,((~r(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(z)), elem!1)) | b(s(z), elem!1) | (~r(s(z), s(s(s(z))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(3344,plain,
% 1.34/1.51 (~r(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[3343, 2266, 537, 3288, 1331, 340, 3320, 448])).
% 1.34/1.51 tff(3345,plain,
% 1.34/1.51 (b(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[289, 3344])).
% 1.34/1.51 tff(3346,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3347,plain,
% 1.34/1.51 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(3348,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3347])).
% 1.34/1.52 tff(3349,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3348, 3346])).
% 1.34/1.52 tff(3350,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(3351,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3350, 3349])).
% 1.34/1.52 tff(3352,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3351, 116, 3345, 2266, 2247, 3279, 28])).
% 1.34/1.52 tff(3353,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | b(s(z), elem!1) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3354,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3353, 3275, 28, 2234, 3277, 340, 448, 2399, 26])).
% 1.34/1.52 tff(3355,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[247, 3354])).
% 1.34/1.52 tff(3356,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3326, 3330])).
% 1.34/1.52 tff(3357,plain,
% 1.34/1.52 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[27, 3356])).
% 1.34/1.52 tff(3358,plain,
% 1.34/1.52 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3330])).
% 1.34/1.52 tff(3359,plain,
% 1.34/1.52 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3322])).
% 1.34/1.52 tff(3360,plain,
% 1.34/1.52 (~b(z, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2255, 254, 28, 2247])).
% 1.34/1.52 tff(3361,plain,
% 1.34/1.52 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[267, 21, 3360])).
% 1.34/1.52 tff(3362,plain,
% 1.34/1.52 (r(z, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3361, 253])).
% 1.34/1.52 tff(3363,plain,
% 1.34/1.52 (~r(s(z), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[301, 293, 3362])).
% 1.34/1.52 tff(3364,plain,
% 1.34/1.52 (b(s(z), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[194, 3363])).
% 1.34/1.52 tff(3365,plain,
% 1.34/1.52 (b(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3364, 3359])).
% 1.34/1.52 tff(3366,plain,
% 1.34/1.52 (b(elem!1, s(s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3365, 3358])).
% 1.34/1.52 tff(3367,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3322])).
% 1.34/1.52 tff(3368,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2016, 3322, 28])).
% 1.34/1.52 tff(3369,plain,
% 1.34/1.52 (b(s(s(elem!1)), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2832, 3322, 2247])).
% 1.34/1.52 tff(3370,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3371,plain,
% 1.34/1.52 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3372,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3371])).
% 1.34/1.52 tff(3373,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3372, 3370])).
% 1.34/1.52 tff(3374,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(3375,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3374, 3373])).
% 1.34/1.52 tff(3376,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3375, 116, 668, 573, 2023, 254])).
% 1.34/1.52 tff(3377,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3378,plain,
% 1.34/1.52 (~b(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3377, 3369, 254, 3368])).
% 1.34/1.52 tff(3379,plain,
% 1.34/1.52 (r(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[514, 3378])).
% 1.34/1.52 tff(3380,plain,
% 1.34/1.52 (~r(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3185, 3379, 293])).
% 1.34/1.52 tff(3381,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[808, 3380])).
% 1.34/1.52 tff(3382,plain,
% 1.34/1.52 (b(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3381, 3367])).
% 1.34/1.52 tff(3383,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3384,plain,
% 1.34/1.52 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3385,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3384])).
% 1.34/1.52 tff(3386,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3385, 3383])).
% 1.34/1.52 tff(3387,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(3388,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3387, 3386])).
% 1.34/1.52 tff(3389,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3388, 116, 3382, 3366, 3329, 3357])).
% 1.34/1.52 tff(3390,plain,((~r(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3391,plain,
% 1.34/1.52 (~r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3390, 3355, 2395, 3277, 2234, 28, 340, 448])).
% 1.34/1.52 tff(3392,plain,
% 1.34/1.52 (b(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[289, 3391])).
% 1.34/1.52 tff(3393,plain,
% 1.34/1.52 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[279, 3392, 3355, 2399])).
% 1.34/1.52 tff(3394,plain,
% 1.34/1.52 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[325, 3393])).
% 1.34/1.52 tff(3395,plain,
% 1.34/1.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[336, 3394, 156])).
% 1.34/1.52 tff(3396,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[149, 3395])).
% 1.34/1.52 tff(3397,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3118, 116, 3392, 2234, 2395, 3396, 28])).
% 1.34/1.52 tff(3398,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), elem!1) | (~r(z, elem!1)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3399,plain,
% 1.34/1.52 (~r(s(z), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3398, 2396, 340, 28, 2])).
% 1.34/1.52 tff(3400,plain,
% 1.34/1.52 (b(s(z), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[172, 3399])).
% 1.34/1.52 tff(3401,plain,
% 1.34/1.52 (~(s(s(z)) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[376, 3400, 340])).
% 1.34/1.52 tff(3402,plain,
% 1.34/1.52 (b(s(s(z)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[426, 3401, 2397])).
% 1.34/1.52 tff(3403,plain,
% 1.34/1.52 (~r(s(s(z)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[456, 448, 66])).
% 1.34/1.52 tff(3404,plain,
% 1.34/1.52 (~(s(s(z)) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[376, 174, 340])).
% 1.34/1.52 tff(3405,plain,
% 1.34/1.52 (b(s(s(z)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[426, 3404, 3403])).
% 1.34/1.52 tff(3406,plain,
% 1.34/1.52 (r(s(z), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[210, 1989])).
% 1.34/1.52 tff(3407,plain,
% 1.34/1.52 (~r(s(z), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2815, 155, 575])).
% 1.34/1.52 tff(3408,plain,
% 1.34/1.52 (s(z) = elem!1),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[357, 3407, 340])).
% 1.34/1.52 tff(3409,plain,
% 1.34/1.52 (r(z, s(z)) <=> r(z, elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3408])).
% 1.34/1.52 tff(3410,plain,
% 1.34/1.52 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3408])).
% 1.34/1.52 tff(3411,plain,
% 1.34/1.52 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[3410])).
% 1.34/1.52 tff(3412,plain,
% 1.34/1.52 (b(s(s(z)), s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1331, 3411])).
% 1.34/1.52 tff(3413,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2282, 3412, 174, 155, 66])).
% 1.34/1.52 tff(3414,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[247, 3413])).
% 1.34/1.52 tff(3415,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3416,plain,
% 1.34/1.52 (((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3417,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3416])).
% 1.34/1.52 tff(3418,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3417, 3415])).
% 1.34/1.52 tff(3419,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(3420,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3419, 3418])).
% 1.34/1.52 tff(3421,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3420, 116, 271, 2247, 28, 254, 174])).
% 1.34/1.52 tff(3422,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3423,plain,
% 1.34/1.52 (~b(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3422, 3414, 28, 2247, 174])).
% 1.34/1.52 tff(3424,plain,
% 1.34/1.52 (r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[289, 3423])).
% 1.34/1.52 tff(3425,plain,
% 1.34/1.52 (r(z, elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3424, 3409])).
% 1.34/1.52 tff(3426,plain,
% 1.34/1.52 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1531, 3408])).
% 1.34/1.52 tff(3427,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2016, 3408, 28])).
% 1.34/1.52 tff(3428,plain,
% 1.34/1.52 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3408])).
% 1.34/1.52 tff(3429,plain,
% 1.34/1.52 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3428, 1093])).
% 1.34/1.52 tff(3430,plain,
% 1.34/1.52 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3429])).
% 1.34/1.52 tff(3431,plain,
% 1.34/1.52 (~(elem!1 = s(s(elem!1)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[566, 3430])).
% 1.34/1.52 tff(3432,plain,
% 1.34/1.52 (b(s(s(elem!1)), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2832, 3408, 2247])).
% 1.34/1.52 tff(3433,plain,
% 1.34/1.52 (~b(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3377, 3432, 3427, 3414])).
% 1.34/1.52 tff(3434,plain,
% 1.34/1.52 (r(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[514, 3433])).
% 1.34/1.52 tff(3435,plain,
% 1.34/1.52 (~r(elem!1, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[502, 3434, 3425])).
% 1.34/1.52 tff(3436,plain,
% 1.34/1.52 (b(elem!1, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1892, 3435, 3431])).
% 1.34/1.52 tff(3437,plain,
% 1.34/1.52 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3428])).
% 1.34/1.52 tff(3438,plain,
% 1.34/1.52 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[566, 3437])).
% 1.34/1.52 tff(3439,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1433, 77, 448, 752, 494])).
% 1.34/1.52 tff(3440,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3441,plain,
% 1.34/1.52 (~r(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3440, 3434, 3425])).
% 1.34/1.52 tff(3442,plain,
% 1.34/1.52 (b(s(s(elem!1)), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[743, 3441, 3438])).
% 1.34/1.52 tff(3443,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3444,plain,
% 1.34/1.52 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3445,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3444])).
% 1.34/1.52 tff(3446,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3445, 3443])).
% 1.34/1.52 tff(3447,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(3448,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3447, 3446])).
% 1.34/1.52 tff(3449,plain,
% 1.34/1.52 (~b(elem!1, s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3448, 116, 3442, 3436, 3427])).
% 1.34/1.52 tff(3450,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3451,plain,
% 1.34/1.52 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3452,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3451])).
% 1.34/1.52 tff(3453,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3452, 3450])).
% 1.34/1.52 tff(3454,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(3455,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.34/1.52 tff(3456,plain,
% 1.34/1.52 (~b(s(s(s(s(z)))), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3455, 116, 3442, 3436, 3427])).
% 1.34/1.52 tff(3457,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3103, 3456, 3449, 28, 2247, 575, 3426, 3425])).
% 1.34/1.52 tff(3458,plain,((~r(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(elem!1, z)) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3459,plain,
% 1.34/1.52 (~r(elem!1, z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3458, 3406, 2247, 28, 340, 66, 3405, 174])).
% 1.34/1.52 tff(3460,plain,
% 1.34/1.52 (b(elem!1, z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[545, 3459, 439])).
% 1.34/1.52 tff(3461,plain,
% 1.34/1.52 (~r(s(z), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[690, 3406, 448])).
% 1.34/1.52 tff(3462,plain,
% 1.34/1.52 (s(z) = elem!1),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[357, 3461, 340])).
% 1.34/1.52 tff(3463,plain,
% 1.34/1.52 (elem!1 = s(z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1984, 3462])).
% 1.34/1.52 tff(3464,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1992, 3463, 3460, 1989])).
% 1.34/1.52 tff(3465,plain,(b(s(z), z) | (elem!1 = z) | b(s(z), elem!1) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(3466,plain,
% 1.34/1.52 (b(s(z), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3465, 439, 340, 2234, 28, 26, 3400, 2396])).
% 1.34/1.52 tff(3467,plain,
% 1.34/1.52 (~(elem!1 = s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2407, 1455, 2247])).
% 1.34/1.52 tff(3468,plain,
% 1.34/1.52 (~(s(z) = elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1458, 1455, 270])).
% 1.34/1.52 tff(3469,plain,
% 1.34/1.52 (r(s(z), elem!1)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[357, 3468, 340])).
% 1.34/1.52 tff(3470,plain,
% 1.34/1.52 (r(elem!1, z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[545, 1455, 439])).
% 1.34/1.52 tff(3471,plain,
% 1.34/1.52 (~r(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3062, 3470, 2247, 448, 3469])).
% 1.34/1.52 tff(3472,plain,
% 1.34/1.52 (b(elem!1, s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1345, 3471, 3467])).
% 1.34/1.52 tff(3473,plain,
% 1.34/1.52 (~r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[3295, 3469, 448])).
% 1.34/1.52 tff(3474,plain,
% 1.34/1.52 (b(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[289, 3473])).
% 1.34/1.52 tff(3475,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3476,plain,
% 1.34/1.52 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(3477,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[3476])).
% 1.34/1.52 tff(3478,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[3477, 3475])).
% 1.34/1.52 tff(3479,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(3480,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[3479, 3478])).
% 1.34/1.53 tff(3481,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3480, 116, 3474, 2247, 3472, 27, 1331])).
% 1.34/1.53 tff(3482,plain,(b(elem!1, z) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~r(z, elem!1)) | b(s(z), elem!1) | (elem!1 = z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3483,plain,
% 1.34/1.53 (b(elem!1, z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3482, 3402, 2395, 2234, 2396, 340, 439, 3466])).
% 1.34/1.53 tff(3484,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3353, 3483, 28, 2234, 3402, 340, 2396, 3466, 26])).
% 1.34/1.53 tff(3485,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[247, 3484])).
% 1.34/1.53 tff(3486,plain,
% 1.34/1.53 (~r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3390, 3485, 2395, 3402, 2234, 28, 340, 2396])).
% 1.34/1.53 tff(3487,plain,
% 1.34/1.53 (~b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3422, 3485, 28, 2234, 3400])).
% 1.34/1.53 tff(3488,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[289, 3487, 3486])).
% 1.34/1.53 tff(3489,plain,((elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), elem!1) | b(s(s(z)), z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3490,plain,
% 1.34/1.53 (elem!1 = z),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3489, 340, 28, 2, 2217])).
% 1.34/1.53 tff(3491,plain,
% 1.34/1.53 (~b(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[409, 3490, 340])).
% 1.34/1.53 tff(3492,plain,
% 1.34/1.53 (r(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[210, 3491])).
% 1.34/1.53 tff(3493,plain,
% 1.34/1.53 (~r(s(z), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[164, 3492, 26])).
% 1.34/1.53 tff(3494,plain,
% 1.34/1.53 (b(s(z), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[172, 3493])).
% 1.34/1.53 tff(3495,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2285, 3492, 26])).
% 1.34/1.53 tff(3496,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[247, 3495])).
% 1.34/1.53 tff(3497,plain,
% 1.34/1.53 (r(s(s(z)), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1685, 404, 2])).
% 1.34/1.53 tff(3498,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2434])).
% 1.34/1.53 tff(3499,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[3498, 1580])).
% 1.34/1.53 tff(3500,plain,
% 1.34/1.53 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3499])).
% 1.34/1.53 tff(3501,plain,
% 1.34/1.53 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[242, 3500])).
% 1.34/1.53 tff(3502,plain,
% 1.34/1.53 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2434])).
% 1.34/1.53 tff(3503,plain,
% 1.34/1.53 ((~b(z, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3502])).
% 1.34/1.53 tff(3504,plain,
% 1.34/1.53 (~b(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3100, 28, 2247, 254])).
% 1.34/1.53 tff(3505,plain,
% 1.34/1.53 (~b(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3504, 3503])).
% 1.34/1.53 tff(3506,plain,
% 1.34/1.53 (r(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1068, 3505, 3501])).
% 1.34/1.53 tff(3507,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[437, 3506, 428])).
% 1.34/1.53 tff(3508,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[149, 3507])).
% 1.34/1.53 tff(3509,plain,
% 1.34/1.53 (r(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2440, 3506, 404])).
% 1.34/1.53 tff(3510,plain,
% 1.34/1.53 (~b(z, s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2450, 3508, 2247, 28, 254])).
% 1.34/1.53 tff(3511,plain,
% 1.34/1.53 (r(z, s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1174, 3510])).
% 1.34/1.53 tff(3512,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1572, 3511, 3509])).
% 1.34/1.53 tff(3513,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[226, 3512])).
% 1.34/1.53 tff(3514,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3515,plain,
% 1.34/1.53 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), 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(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3516,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3515])).
% 1.34/1.53 tff(3517,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[3516, 3514])).
% 1.34/1.53 tff(3518,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(3519,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3518, 3517])).
% 1.34/1.53 tff(3520,plain,
% 1.34/1.53 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3519, 116, 3513, 3508, 174])).
% 1.34/1.53 tff(3521,plain,
% 1.34/1.53 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[323, 21, 320, 3520])).
% 1.34/1.53 tff(3522,plain,
% 1.34/1.53 (~b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3422, 28, 2247, 254, 174])).
% 1.34/1.53 tff(3523,plain,
% 1.34/1.53 (r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[289, 3522])).
% 1.34/1.53 tff(3524,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2367, 77, 3523, 3509, 3521])).
% 1.34/1.53 tff(3525,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3526,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3525, 3497, 404, 2234, 28, 174, 254])).
% 1.34/1.53 tff(3527,plain,((~(elem!1 = z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3528,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3527, 3496, 3494, 28, 3490, 2])).
% 1.34/1.53 tff(3529,plain,(b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3530,plain,
% 1.34/1.53 (b(s(z), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3529, 2217, 2, 28])).
% 1.34/1.53 tff(3531,plain,
% 1.34/1.53 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[442])).
% 1.34/1.53 tff(3532,plain,
% 1.34/1.53 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[3531])).
% 1.34/1.53 tff(3533,plain,
% 1.34/1.53 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[442])).
% 1.34/1.53 tff(3534,plain,
% 1.34/1.53 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.34/1.53 inference(symmetry,[status(thm)],[3533])).
% 1.34/1.53 tff(3535,plain,
% 1.34/1.53 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3534])).
% 1.34/1.53 tff(3536,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(3537,plain,
% 1.34/1.53 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(quant_intro,[status(thm)],[3536])).
% 1.34/1.53 tff(3538,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(3539,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.34/1.53 tff(3540,plain,
% 1.34/1.53 (![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3539, 3538])).
% 1.34/1.53 tff(3541,plain,(
% 1.34/1.53 ![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(skolemize,[status(sab)],[3540])).
% 1.34/1.53 tff(3542,plain,
% 1.34/1.53 (![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3541, 3537])).
% 1.34/1.53 tff(3543,plain,
% 1.34/1.53 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(3544,plain,
% 1.34/1.53 (~b(elem!1, elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3543, 3542])).
% 1.34/1.53 tff(3545,plain,
% 1.34/1.53 (~b(elem!1, z)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3544, 3535])).
% 1.34/1.53 tff(3546,plain,
% 1.34/1.53 (~(elem!1 = s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2407, 3545, 2234])).
% 1.34/1.53 tff(3547,plain,
% 1.34/1.53 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[442])).
% 1.34/1.53 tff(3548,plain,
% 1.34/1.53 (b(s(s(s(z))), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2234, 3547])).
% 1.34/1.53 tff(3549,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2395, 1943])).
% 1.34/1.53 tff(3550,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1792])).
% 1.34/1.53 tff(3551,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[3550])).
% 1.34/1.53 tff(3552,plain,
% 1.34/1.53 (r(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[247, 239])).
% 1.34/1.53 tff(3553,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[237, 3552, 66])).
% 1.34/1.53 tff(3554,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[226, 3553])).
% 1.34/1.53 tff(3555,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2578])).
% 1.34/1.53 tff(3556,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[3555])).
% 1.34/1.53 tff(3557,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[212, 3556])).
% 1.34/1.53 tff(3558,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2014, 3557])).
% 1.34/1.53 tff(3559,plain,((~b(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(z)))), s(s(elem!1))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3560,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3559, 3554, 1713])).
% 1.34/1.53 tff(3561,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.34/1.53 tff(3562,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(3563,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3564,plain,
% 1.34/1.53 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3565,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3564])).
% 1.34/1.53 tff(3566,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[3565, 3563])).
% 1.34/1.53 tff(3567,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(3568,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 1.34/1.53 tff(3569,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3568, 116, 3561, 1054, 28, 2023, 3562])).
% 1.34/1.53 tff(3570,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3571,plain,
% 1.34/1.53 (~b(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3570, 3560, 28, 3561, 1944])).
% 1.34/1.53 tff(3572,plain,
% 1.34/1.53 (r(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1068, 3571, 1718])).
% 1.34/1.53 tff(3573,plain,
% 1.34/1.53 (r(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2440, 3572, 1713])).
% 1.34/1.53 tff(3574,plain,
% 1.34/1.53 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1793])).
% 1.34/1.53 tff(3575,plain,
% 1.34/1.53 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.34/1.53 inference(symmetry,[status(thm)],[1580])).
% 1.34/1.53 tff(3576,plain,
% 1.34/1.53 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.34/1.53 inference(transitivity,[status(thm)],[1716, 3575])).
% 1.34/1.53 tff(3577,plain,
% 1.34/1.53 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3576])).
% 1.34/1.53 tff(3578,plain,
% 1.34/1.53 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[242, 3577])).
% 1.34/1.53 tff(3579,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[404])).
% 1.34/1.53 tff(3580,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1725, 3579])).
% 1.34/1.53 tff(3581,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[239, 3580])).
% 1.34/1.53 tff(3582,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3583,plain,
% 1.34/1.53 (~b(s(s(s(s(z)))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3582, 239, 1713])).
% 1.34/1.53 tff(3584,plain,
% 1.34/1.53 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1596, 3583, 3578])).
% 1.34/1.53 tff(3585,plain,
% 1.34/1.53 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1603, 77, 752, 3584])).
% 1.34/1.53 tff(3586,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3585, 3574])).
% 1.34/1.53 tff(3587,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[149, 3586])).
% 1.34/1.53 tff(3588,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3587, 3551])).
% 1.34/1.53 tff(3589,assumption,(b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.53 tff(3590,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3591,plain,
% 1.34/1.53 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3592,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3591])).
% 1.34/1.53 tff(3593,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[3592, 3590])).
% 1.34/1.53 tff(3594,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(3595,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3594, 3593])).
% 1.34/1.53 tff(3596,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3595, 116, 3561, 28, 1177, 3562, 3589])).
% 1.34/1.53 tff(3597,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3598,plain,
% 1.34/1.53 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3597, 1944, 28, 3561, 3588])).
% 1.34/1.53 tff(3599,plain,
% 1.34/1.53 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1146, 3598])).
% 1.34/1.53 tff(3600,plain,
% 1.34/1.53 (~r(z, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2461, 3599, 3573])).
% 1.34/1.53 tff(3601,plain,
% 1.34/1.53 (~r(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2488, 3600, 1713])).
% 1.34/1.53 tff(3602,plain,
% 1.34/1.53 (b(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1345, 3601, 1620])).
% 1.34/1.53 tff(3603,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3604,plain,
% 1.34/1.53 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(3605,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[3604])).
% 1.34/1.53 tff(3606,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[3605, 3603])).
% 1.34/1.53 tff(3607,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(3608,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 1.34/1.53 tff(3609,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3608, 116, 3561, 3602, 28, 3560, 1944])).
% 1.34/1.53 tff(3610,plain,(b(s(s(s(s(z)))), z) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~(z = elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3611,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3610, 3548, 28, 3546, 442, 2395, 1825, 26])).
% 1.34/1.53 tff(3612,plain,
% 1.34/1.53 (~b(s(z), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3527, 3611, 28, 1713, 2])).
% 1.34/1.53 tff(3613,plain,
% 1.34/1.53 (r(s(z), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[172, 3612])).
% 1.34/1.53 tff(3614,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3611, 1719])).
% 1.34/1.53 tff(3615,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1737, 3614, 28, 1714, 847, 3613, 1718])).
% 1.34/1.53 tff(3616,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[149, 3615])).
% 1.34/1.53 tff(3617,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3616, 3551])).
% 1.34/1.53 tff(3618,plain,
% 1.34/1.53 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3597, 3617, 28, 3549, 3548])).
% 1.34/1.53 tff(3619,plain,
% 1.34/1.53 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1146, 3618])).
% 1.34/1.53 tff(3620,plain,
% 1.34/1.53 (~b(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3100, 3611, 2234, 28])).
% 1.34/1.53 tff(3621,plain,
% 1.34/1.53 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[442])).
% 1.34/1.53 tff(3622,plain,
% 1.34/1.53 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[3621])).
% 1.34/1.53 tff(3623,plain,
% 1.34/1.53 (b(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1054, 3622])).
% 1.34/1.53 tff(3624,assumption,(~b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.53 tff(3625,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3624, 3623])).
% 1.34/1.53 tff(3626,plain,((~b(elem!1, s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3627,plain,
% 1.34/1.53 (~b(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3626, 3620, 442])).
% 1.34/1.53 tff(3628,plain,
% 1.34/1.53 (r(elem!1, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1068, 3627, 1718])).
% 1.34/1.53 tff(3629,plain,
% 1.34/1.53 (r(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2440, 3628, 1713])).
% 1.34/1.53 tff(3630,plain,
% 1.34/1.53 (~r(z, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2461, 3629, 3619])).
% 1.34/1.53 tff(3631,plain,
% 1.34/1.53 (~r(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2488, 3630, 1713])).
% 1.34/1.53 tff(3632,plain,
% 1.34/1.53 (b(elem!1, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1345, 3631, 3546])).
% 1.34/1.53 tff(3633,plain,
% 1.34/1.53 (b(z, s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[3632, 3532])).
% 1.34/1.53 tff(3634,plain,
% 1.34/1.53 (~b(z, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2255, 3611, 28, 2234])).
% 1.34/1.53 tff(3635,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3634, 3633])).
% 1.34/1.53 tff(3636,plain,((~(z = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3637,plain,
% 1.34/1.53 (~(z = elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3636, 3530, 28, 2])).
% 1.34/1.53 tff(3638,plain,
% 1.34/1.53 (r(z, elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1044, 3637, 2217])).
% 1.34/1.53 tff(3639,plain,
% 1.34/1.53 (~b(s(z), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3422, 271, 28, 2247, 254])).
% 1.34/1.53 tff(3640,plain,
% 1.34/1.53 (r(s(z), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[172, 3639])).
% 1.34/1.53 tff(3641,plain,
% 1.34/1.53 (~r(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[164, 3640, 66])).
% 1.34/1.53 tff(3642,plain,
% 1.34/1.53 (b(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[210, 3641])).
% 1.34/1.53 tff(3643,plain,
% 1.34/1.53 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[279, 3642, 254, 271])).
% 1.34/1.53 tff(3644,plain,
% 1.34/1.53 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[325, 3643])).
% 1.34/1.53 tff(3645,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[336, 3644, 3640])).
% 1.34/1.53 tff(3646,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[149, 3645])).
% 1.34/1.53 tff(3647,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3118, 116, 271, 2247, 3279, 3646, 28])).
% 1.34/1.53 tff(3648,plain,((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(3649,plain,
% 1.34/1.53 (~b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[3648, 254, 28, 2234, 26])).
% 1.34/1.54 tff(3650,plain,
% 1.34/1.54 (r(z, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[289, 3649])).
% 1.34/1.54 tff(3651,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.34/1.54 tff(3652,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3653,plain,
% 1.34/1.54 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3654,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3653])).
% 1.34/1.54 tff(3655,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[3654, 3652])).
% 1.34/1.54 tff(3656,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(3657,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3656, 3655])).
% 1.34/1.54 tff(3658,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3657, 77, 293, 66, 3651])).
% 1.34/1.54 tff(3659,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3660,plain,
% 1.34/1.54 (~r(s(s(z)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3659, 3650, 26])).
% 1.34/1.54 tff(3661,plain,
% 1.34/1.54 (~(z = elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3636, 847, 28, 2])).
% 1.34/1.54 tff(3662,plain,
% 1.34/1.54 (~b(z, s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3100, 254, 2234, 28])).
% 1.34/1.54 tff(3663,plain,
% 1.34/1.54 (s(z) = elem!1),
% 1.34/1.54 inference(symmetry,[status(thm)],[417])).
% 1.34/1.54 tff(3664,plain,
% 1.34/1.54 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3663])).
% 1.34/1.54 tff(3665,plain,
% 1.34/1.54 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[3664])).
% 1.34/1.54 tff(3666,plain,
% 1.34/1.54 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3665])).
% 1.34/1.54 tff(3667,plain,
% 1.34/1.54 (~b(s(z), elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3544, 3666])).
% 1.34/1.54 tff(3668,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[847, 3667])).
% 1.34/1.54 tff(3669,plain,((~(elem!1 = s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3670,plain,
% 1.34/1.54 (~(elem!1 = s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3669, 847])).
% 1.34/1.54 tff(3671,plain,
% 1.34/1.54 (~(s(z) = elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1984, 3670])).
% 1.34/1.54 tff(3672,plain,
% 1.34/1.54 (s(s(z)) = elem!1),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[426, 1, 1673])).
% 1.34/1.54 tff(3673,plain,
% 1.34/1.54 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[529, 3672, 518])).
% 1.34/1.54 tff(3674,plain,
% 1.34/1.54 (s(s(s(z))) = s(elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3672])).
% 1.34/1.54 tff(3675,plain,
% 1.34/1.54 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3674])).
% 1.34/1.54 tff(3676,plain,
% 1.34/1.54 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3675])).
% 1.34/1.54 tff(3677,plain,
% 1.34/1.54 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3676])).
% 1.34/1.54 tff(3678,plain,
% 1.34/1.54 (~b(z, s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3624, 3677])).
% 1.34/1.54 tff(3679,plain,
% 1.34/1.54 (r(z, s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[514, 3678])).
% 1.34/1.54 tff(3680,plain,
% 1.34/1.54 (~r(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3440, 3679, 448])).
% 1.34/1.54 tff(3681,plain,
% 1.34/1.54 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[3675])).
% 1.34/1.54 tff(3682,plain,
% 1.34/1.54 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3681])).
% 1.34/1.54 tff(3683,plain,
% 1.34/1.54 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[3682])).
% 1.34/1.54 tff(3684,plain,
% 1.34/1.54 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3672])).
% 1.34/1.54 tff(3685,plain,
% 1.34/1.54 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1039, 1, 2, 448, 254, 518])).
% 1.34/1.54 tff(3686,plain,
% 1.34/1.54 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[149, 3685])).
% 1.34/1.54 tff(3687,plain,
% 1.34/1.54 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3686, 3684])).
% 1.34/1.54 tff(3688,plain,
% 1.34/1.54 (b(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3687, 3683])).
% 1.34/1.54 tff(3689,plain,
% 1.34/1.54 (~r(s(s(elem!1)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3185, 293, 494])).
% 1.34/1.54 tff(3690,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[808, 3689])).
% 1.34/1.54 tff(3691,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3692,plain,
% 1.34/1.54 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3693,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3692])).
% 1.34/1.54 tff(3694,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[3693, 3691])).
% 1.34/1.54 tff(3695,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(3696,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3695, 3694])).
% 1.34/1.54 tff(3697,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3696, 116, 1436, 616, 847, 1879])).
% 1.34/1.54 tff(3698,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3699,plain,
% 1.34/1.54 (~b(s(z), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3698, 3690, 1879, 616])).
% 1.34/1.54 tff(3700,plain,
% 1.34/1.54 (r(s(z), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[357, 3699, 353])).
% 1.34/1.54 tff(3701,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2916, 77, 448, 3700, 293])).
% 1.34/1.54 tff(3702,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3703,plain,
% 1.34/1.54 (~b(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3702, 3679, 448, 353, 3688, 293])).
% 1.34/1.54 tff(3704,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[743, 3703, 3680, 3673])).
% 1.34/1.54 tff(3705,plain,(b(s(s(z)), elem!1) | (~r(z, elem!1)) | (s(z) = elem!1) | (~r(z, s(z))) | b(z, s(s(s(s(z))))) | (z = elem!1) | b(s(s(z)), z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3706,plain,
% 1.34/1.54 (b(s(s(z)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3705, 3650, 3671, 448, 3662, 3661, 2, 254])).
% 1.34/1.54 tff(3707,plain,
% 1.34/1.54 (~r(elem!1, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[791, 3650, 448])).
% 1.34/1.54 tff(3708,plain,
% 1.34/1.54 (b(elem!1, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[633, 3707, 3670])).
% 1.34/1.54 tff(3709,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3710,plain,
% 1.34/1.54 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3711,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3710])).
% 1.34/1.54 tff(3712,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[3711, 3709])).
% 1.34/1.54 tff(3713,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(3714,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 1.34/1.54 tff(3715,plain,
% 1.34/1.54 (~b(s(s(z)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3714, 116, 847, 3708, 3706])).
% 1.34/1.54 tff(3716,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[391, 21, 3715, 388, 3660])).
% 1.34/1.54 tff(3717,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | b(s(s(z)), z) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3718,plain,
% 1.34/1.54 (~b(s(s(s(s(z)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3717, 3530, 3638, 2, 28])).
% 1.34/1.54 tff(3719,plain,
% 1.34/1.54 (r(s(s(s(s(z)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[247, 3718])).
% 1.34/1.54 tff(3720,plain,
% 1.34/1.54 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[237, 3719, 26])).
% 1.34/1.54 tff(3721,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[226, 3720])).
% 1.34/1.54 tff(3722,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3351, 116, 271, 212, 2247, 27, 28])).
% 1.34/1.54 tff(3723,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3724,plain,
% 1.34/1.54 (~b(z, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3723, 3721, 2234, 2395, 28])).
% 1.34/1.54 tff(3725,plain,
% 1.34/1.54 (r(z, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[289, 3724])).
% 1.34/1.54 tff(3726,plain,
% 1.34/1.54 (~r(s(s(z)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3659, 3725, 26])).
% 1.34/1.54 tff(3727,plain,
% 1.34/1.54 (~r(s(s(z)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[456, 3638, 26])).
% 1.34/1.54 tff(3728,plain,
% 1.34/1.54 (~(elem!1 = z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[533, 3637])).
% 1.34/1.54 tff(3729,plain,
% 1.34/1.54 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[237, 228, 26])).
% 1.34/1.54 tff(3730,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[226, 3729])).
% 1.34/1.54 tff(3731,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3732,plain,
% 1.34/1.54 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3733,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3732])).
% 1.34/1.54 tff(3734,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[3733, 3731])).
% 1.34/1.54 tff(3735,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(3736,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 1.34/1.54 tff(3737,plain,
% 1.34/1.54 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3736, 77, 26, 228])).
% 1.34/1.54 tff(3738,plain,
% 1.34/1.54 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[149, 3737])).
% 1.34/1.54 tff(3739,plain,
% 1.34/1.54 (~r(elem!1, s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2671, 2806, 228])).
% 1.34/1.54 tff(3740,plain,
% 1.34/1.54 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1068, 3739, 1362])).
% 1.34/1.54 tff(3741,plain,
% 1.34/1.54 (~r(s(z), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2285, 228, 26])).
% 1.34/1.54 tff(3742,plain,
% 1.34/1.54 (b(s(z), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[210, 3741])).
% 1.34/1.54 tff(3743,plain,
% 1.34/1.54 (~(s(z) = elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1458, 1455, 3742])).
% 1.34/1.54 tff(3744,plain,
% 1.34/1.54 (~r(s(s(s(s(z)))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2650, 2806, 228])).
% 1.34/1.54 tff(3745,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1596, 3744, 2416])).
% 1.34/1.54 tff(3746,plain,
% 1.34/1.54 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[486])).
% 1.34/1.54 tff(3747,plain,
% 1.34/1.54 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[3746])).
% 1.34/1.54 tff(3748,plain,
% 1.34/1.54 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[458])).
% 1.34/1.54 tff(3749,plain,
% 1.34/1.54 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[3748])).
% 1.34/1.54 tff(3750,plain,
% 1.34/1.54 (b(s(z), s(s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[847, 3749])).
% 1.34/1.54 tff(3751,plain,
% 1.34/1.54 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[485])).
% 1.34/1.54 tff(3752,plain,
% 1.34/1.54 (b(s(elem!1), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2247, 3751])).
% 1.34/1.54 tff(3753,plain,
% 1.34/1.54 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[487])).
% 1.34/1.54 tff(3754,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(symmetry,[status(thm)],[3753])).
% 1.34/1.54 tff(3755,plain,
% 1.34/1.54 (b(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1725, 3754])).
% 1.34/1.54 tff(3756,plain,
% 1.34/1.54 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1364, 1362])).
% 1.34/1.54 tff(3757,plain,
% 1.34/1.54 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[370])).
% 1.34/1.54 tff(3758,plain,
% 1.34/1.54 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.34/1.54 inference(symmetry,[status(thm)],[3757])).
% 1.34/1.54 tff(3759,plain,
% 1.34/1.54 (b(s(s(z)), s(z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2060, 3758])).
% 1.34/1.54 tff(3760,plain,
% 1.34/1.54 (~b(s(s(z)), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2282, 155, 174, 228, 66])).
% 1.34/1.54 tff(3761,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3760, 3759])).
% 1.34/1.54 tff(3762,plain,((~r(s(z), z)) | (~(s(s(z)) = elem!1)) | (elem!1 = s(z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(3763,plain,
% 1.34/1.54 (~r(s(z), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3762, 228, 1046, 2036, 370, 66, 575])).
% 1.34/1.54 tff(3764,plain,
% 1.34/1.54 (b(s(z), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[210, 3763])).
% 1.34/1.54 tff(3765,plain,
% 1.34/1.54 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.34/1.54 inference(commutativity,[status(thm)],[])).
% 1.34/1.54 tff(3766,plain,
% 1.34/1.54 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[3765])).
% 1.34/1.54 tff(3767,plain,
% 1.34/1.54 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3766])).
% 1.34/1.54 tff(3768,plain,
% 1.34/1.54 (~(z = s(s(s(s(s(z))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[895, 3767])).
% 1.34/1.54 tff(3769,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3770,plain,
% 1.34/1.54 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3771,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3770])).
% 1.34/1.54 tff(3772,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[3771, 3769])).
% 1.34/1.54 tff(3773,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(3774,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 1.34/1.54 tff(3775,plain,
% 1.34/1.54 (~r(z, s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3774, 77, 448, 1027])).
% 1.34/1.54 tff(3776,plain,
% 1.34/1.54 (((~![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)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3777,plain,
% 1.34/1.54 ((~![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)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(3778,plain,
% 1.34/1.54 ((~![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))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3777, 3776])).
% 1.34/1.54 tff(3779,plain,
% 1.34/1.54 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3778, 21, 3775])).
% 1.34/1.54 tff(3780,plain,
% 1.34/1.54 (b(z, s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3779, 3768])).
% 1.34/1.54 tff(3781,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3782,plain,
% 1.34/1.54 (((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3783,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[3782])).
% 1.34/1.54 tff(3784,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[3783, 3781])).
% 1.34/1.54 tff(3785,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(3786,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[3785, 3784])).
% 1.34/1.54 tff(3787,plain,
% 1.34/1.54 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[3786, 116, 2844, 1031, 3780])).
% 1.34/1.54 tff(3788,plain,
% 1.34/1.54 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[858, 21, 855, 3787])).
% 1.34/1.54 tff(3789,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(3790,plain,
% 1.34/1.54 (((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3791,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3790])).
% 1.34/1.55 tff(3792,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3791, 3789])).
% 1.34/1.55 tff(3793,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(3794,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3793, 3792])).
% 1.34/1.55 tff(3795,plain,
% 1.34/1.55 (~b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3794, 116, 270, 1031, 3780])).
% 1.34/1.55 tff(3796,plain,
% 1.34/1.55 (r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[870, 21, 867, 3795])).
% 1.34/1.55 tff(3797,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3798,plain,
% 1.34/1.55 (((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3799,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3798])).
% 1.34/1.55 tff(3800,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3799, 3797])).
% 1.34/1.55 tff(3801,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(3802,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 1.34/1.55 tff(3803,plain,
% 1.34/1.55 (~b(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3802, 116, 270, 2844, 1031, 3780])).
% 1.34/1.55 tff(3804,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.34/1.55 tff(3805,plain,
% 1.34/1.55 (r(s(elem!1), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[735, 21, 3804, 3803])).
% 1.34/1.55 tff(3806,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[878, 77, 3805, 3796, 3788])).
% 1.34/1.55 tff(3807,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(z) = s(s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3808,plain,
% 1.34/1.55 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3807, 3764, 829, 843, 2844, 3756, 448])).
% 1.34/1.55 tff(3809,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[885, 3808, 569])).
% 1.34/1.55 tff(3810,plain,
% 1.34/1.55 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[557])).
% 1.34/1.55 tff(3811,plain,
% 1.34/1.55 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(symmetry,[status(thm)],[3810])).
% 1.34/1.55 tff(3812,plain,
% 1.34/1.55 (~r(elem!1, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2671, 228, 575])).
% 1.34/1.55 tff(3813,plain,
% 1.34/1.55 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1068, 3812, 1362])).
% 1.34/1.55 tff(3814,plain,
% 1.34/1.55 (b(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3813, 3811])).
% 1.34/1.55 tff(3815,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3816,plain,
% 1.34/1.55 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3817,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3816])).
% 1.34/1.55 tff(3818,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3817, 3815])).
% 1.34/1.55 tff(3819,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(3820,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3819, 3818])).
% 1.34/1.55 tff(3821,plain,
% 1.34/1.55 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3820, 116, 616, 3814, 3809])).
% 1.34/1.55 tff(3822,plain,
% 1.34/1.55 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[916, 21, 913, 3821])).
% 1.34/1.55 tff(3823,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3824,plain,
% 1.34/1.55 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3825,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3824])).
% 1.34/1.55 tff(3826,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3825, 3823])).
% 1.34/1.55 tff(3827,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(3828,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 1.34/1.55 tff(3829,plain,
% 1.34/1.55 (~b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3828, 116, 616, 847, 3814, 3809])).
% 1.34/1.55 tff(3830,plain,
% 1.34/1.55 (r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[870, 21, 829, 3829])).
% 1.34/1.55 tff(3831,plain,
% 1.34/1.55 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3832,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3831])).
% 1.34/1.55 tff(3833,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3832, 3691])).
% 1.34/1.55 tff(3834,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(3835,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3834, 3833])).
% 1.34/1.55 tff(3836,plain,
% 1.34/1.55 (~b(s(s(elem!1)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3835, 116, 616, 847, 3814])).
% 1.34/1.55 tff(3837,plain,
% 1.34/1.55 (r(s(s(elem!1)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[808, 3836])).
% 1.34/1.55 tff(3838,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[984, 77, 3837, 3830, 3822])).
% 1.34/1.55 tff(3839,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (elem!1 = s(z)) | (~(s(s(z)) = elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3840,plain,
% 1.34/1.55 (~r(s(s(s(s(z)))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3839, 3755, 847, 3752, 448, 421, 458, 26, 575, 1362])).
% 1.34/1.55 tff(3841,plain,
% 1.34/1.55 (b(s(s(s(s(z)))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[247, 3840])).
% 1.34/1.55 tff(3842,plain,
% 1.34/1.55 (~b(z, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3422, 3841, 28, 2247, 3750])).
% 1.34/1.55 tff(3843,plain,
% 1.34/1.55 (r(z, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[289, 3842])).
% 1.34/1.55 tff(3844,plain,
% 1.34/1.55 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[487])).
% 1.34/1.55 tff(3845,plain,
% 1.34/1.55 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(symmetry,[status(thm)],[3844])).
% 1.34/1.55 tff(3846,plain,
% 1.34/1.55 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[458])).
% 1.34/1.55 tff(3847,plain,
% 1.34/1.55 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3846, 3845])).
% 1.34/1.55 tff(3848,plain,
% 1.34/1.55 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1039, 3841, 2, 448, 518, 1])).
% 1.34/1.55 tff(3849,plain,
% 1.34/1.55 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[149, 3848])).
% 1.34/1.55 tff(3850,plain,
% 1.34/1.55 (b(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3849, 3847])).
% 1.34/1.55 tff(3851,plain,
% 1.34/1.55 (~r(z, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3702, 3850, 353, 448, 3755, 3843])).
% 1.34/1.55 tff(3852,plain,
% 1.34/1.55 (b(z, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[514, 3851])).
% 1.34/1.55 tff(3853,plain,
% 1.34/1.55 (b(z, s(s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3852, 3747])).
% 1.34/1.55 tff(3854,plain,
% 1.34/1.55 (~b(z, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3100, 3841, 28, 2247])).
% 1.34/1.55 tff(3855,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3854, 3853])).
% 1.34/1.55 tff(3856,plain,(b(s(s(z)), z) | (s(z) = elem!1) | (~r(z, elem!1)) | (z = elem!1) | b(s(s(z)), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~r(elem!1, z)) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3857,plain,
% 1.34/1.55 (b(s(s(z)), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3856, 3745, 2, 2234, 3743, 28, 847, 1362, 2806, 2396, 446])).
% 1.34/1.55 tff(3858,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2539, 3857, 3740, 3738, 3730])).
% 1.34/1.55 tff(3859,plain,((elem!1 = z) | b(s(s(z)), z) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | b(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3860,plain,
% 1.34/1.55 (elem!1 = s(s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3859, 1455, 28, 2, 3530, 3728, 2217, 228])).
% 1.34/1.55 tff(3861,plain,
% 1.34/1.55 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3860])).
% 1.34/1.55 tff(3862,plain,
% 1.34/1.55 (~b(z, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3723, 3730, 2234, 2395, 28])).
% 1.34/1.55 tff(3863,plain,
% 1.34/1.55 (r(z, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[289, 3862])).
% 1.34/1.55 tff(3864,plain,
% 1.34/1.55 (~r(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[791, 3863, 3638])).
% 1.34/1.55 tff(3865,plain,
% 1.34/1.55 (~(elem!1 = s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[420, 3743])).
% 1.34/1.55 tff(3866,plain,
% 1.34/1.55 (b(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[633, 3865, 3864])).
% 1.34/1.55 tff(3867,plain,
% 1.34/1.55 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3866, 3861])).
% 1.34/1.55 tff(3868,plain,
% 1.34/1.55 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1077])).
% 1.34/1.55 tff(3869,plain,
% 1.34/1.55 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.34/1.55 inference(symmetry,[status(thm)],[3868])).
% 1.34/1.55 tff(3870,plain,
% 1.34/1.55 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), elem!1))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3869])).
% 1.34/1.55 tff(3871,plain,
% 1.34/1.55 (~b(s(z), elem!1)),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[313, 3870])).
% 1.34/1.55 tff(3872,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[847, 3871])).
% 1.34/1.55 tff(3873,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(z), elem!1)) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3874,plain,
% 1.34/1.55 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3873, 3860, 3530])).
% 1.34/1.55 tff(3875,plain,
% 1.34/1.55 (~r(s(s(z)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3659, 3863, 26])).
% 1.34/1.55 tff(3876,plain,
% 1.34/1.55 (b(s(s(z)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[391, 21, 388, 3875])).
% 1.34/1.55 tff(3877,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3878,plain,
% 1.34/1.55 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3879,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3878])).
% 1.34/1.55 tff(3880,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3879, 3877])).
% 1.34/1.55 tff(3881,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(3882,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3881, 3880])).
% 1.34/1.55 tff(3883,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3882, 116, 3730, 3876, 3874, 3867])).
% 1.34/1.55 tff(3884,plain,(b(elem!1, z) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), z) | b(z, elem!1) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3885,plain,
% 1.34/1.55 (b(elem!1, z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3884, 3719, 2, 2217, 28])).
% 1.34/1.55 tff(3886,plain,
% 1.34/1.55 (~(s(s(z)) = elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[540, 3885, 2])).
% 1.34/1.55 tff(3887,plain,
% 1.34/1.55 (b(s(s(z)), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[426, 3886, 3727])).
% 1.34/1.55 tff(3888,plain,
% 1.34/1.55 (~(elem!1 = s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3669, 3530])).
% 1.34/1.55 tff(3889,plain,
% 1.34/1.55 (~r(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[791, 3725, 3638])).
% 1.34/1.55 tff(3890,plain,
% 1.34/1.55 (b(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[633, 3889, 3888])).
% 1.34/1.55 tff(3891,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3892,plain,
% 1.34/1.55 (((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(3893,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[3892])).
% 1.34/1.55 tff(3894,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[3893, 3891])).
% 1.34/1.55 tff(3895,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(3896,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 1.34/1.55 tff(3897,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3896, 116, 537, 847, 667, 1331, 1048])).
% 1.34/1.55 tff(3898,plain,((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3899,plain,
% 1.34/1.55 (~b(s(s(z)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3898, 3890, 3530, 3885, 3887])).
% 1.34/1.55 tff(3900,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[391, 21, 3899, 388, 3726])).
% 1.34/1.55 tff(3901,plain,(b(z, elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(3902,plain,
% 1.34/1.55 (b(z, elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[3901, 28, 2])).
% 1.34/1.55 tff(3903,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3904,plain,
% 1.34/1.56 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3905,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[3904])).
% 1.34/1.56 tff(3906,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[3905, 3903])).
% 1.34/1.56 tff(3907,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(3908,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[3907, 3906])).
% 1.34/1.56 tff(3909,plain,
% 1.34/1.56 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3908, 116, 3902, 2234, 2395, 28])).
% 1.34/1.56 tff(3910,plain,
% 1.34/1.56 (r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[149, 3909])).
% 1.34/1.56 tff(3911,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3912,plain,
% 1.34/1.56 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3913,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[3912])).
% 1.34/1.56 tff(3914,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[3913, 3911])).
% 1.34/1.56 tff(3915,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(3916,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[3915, 3914])).
% 1.34/1.56 tff(3917,plain,
% 1.34/1.56 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3916, 116, 3902, 2234, 2395, 28])).
% 1.34/1.56 tff(3918,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[226, 3917])).
% 1.34/1.56 tff(3919,plain,
% 1.34/1.56 (~r(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[237, 3918, 26])).
% 1.34/1.56 tff(3920,plain,
% 1.34/1.56 (b(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[247, 3919])).
% 1.34/1.56 tff(3921,plain,
% 1.34/1.56 (~b(z, s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3648, 3920, 28, 2234, 26])).
% 1.34/1.56 tff(3922,plain,
% 1.34/1.56 (r(z, s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[289, 3921])).
% 1.34/1.56 tff(3923,plain,
% 1.34/1.56 (~b(z, s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2255, 3920, 28, 2234])).
% 1.34/1.56 tff(3924,plain,
% 1.34/1.56 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[267, 21, 3923])).
% 1.34/1.56 tff(3925,plain,
% 1.34/1.56 (r(z, s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3924, 253])).
% 1.34/1.56 tff(3926,plain,
% 1.34/1.56 (~r(s(z), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[301, 3925, 3922])).
% 1.34/1.56 tff(3927,plain,
% 1.34/1.56 (b(s(z), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[194, 3926])).
% 1.34/1.56 tff(3928,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3929,plain,
% 1.34/1.56 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3930,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[3929])).
% 1.34/1.56 tff(3931,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[3930, 3928])).
% 1.34/1.56 tff(3932,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(3933,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[3932, 3931])).
% 1.34/1.56 tff(3934,plain,
% 1.34/1.56 (~b(s(z), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3933, 116, 3902, 2234, 2395, 3927])).
% 1.34/1.56 tff(3935,plain,
% 1.34/1.56 (r(s(z), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[172, 3934])).
% 1.34/1.56 tff(3936,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3937,plain,
% 1.34/1.56 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3938,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[3937])).
% 1.34/1.56 tff(3939,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[3938, 3936])).
% 1.34/1.56 tff(3940,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(3941,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[3940, 3939])).
% 1.34/1.56 tff(3942,plain,
% 1.34/1.56 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3941, 116, 3902, 2234, 28, 3927])).
% 1.34/1.56 tff(3943,plain,
% 1.34/1.56 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[325, 3942])).
% 1.34/1.56 tff(3944,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[336, 3943, 3935, 3910])).
% 1.34/1.56 tff(3945,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(3946,plain,
% 1.34/1.56 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3945, 2])).
% 1.34/1.56 tff(3947,plain,
% 1.34/1.56 (((~![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)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3948,plain,
% 1.34/1.56 ((~![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)))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(3949,plain,
% 1.34/1.56 ((~![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))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 1.34/1.56 tff(3950,plain,
% 1.34/1.56 ((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))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3949, 21])).
% 1.34/1.56 tff(3951,plain,
% 1.34/1.56 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3950, 1140])).
% 1.34/1.56 tff(3952,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3951, 3946])).
% 1.34/1.56 tff(3953,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.56 tff(3954,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3955,plain,
% 1.34/1.56 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3956,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[3955])).
% 1.34/1.56 tff(3957,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[3956, 3954])).
% 1.34/1.56 tff(3958,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(3959,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[3958, 3957])).
% 1.34/1.56 tff(3960,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3959, 77, 67, 3953, 228])).
% 1.34/1.56 tff(3961,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(3962,plain,
% 1.34/1.56 (~r(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3961, 67, 3952])).
% 1.34/1.56 tff(3963,plain,
% 1.34/1.56 (b(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[247, 3962])).
% 1.34/1.56 tff(3964,plain,
% 1.34/1.56 (~r(s(z), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[203, 67, 26])).
% 1.34/1.56 tff(3965,plain,
% 1.34/1.56 (b(s(z), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[210, 3964])).
% 1.34/1.56 tff(3966,plain,
% 1.34/1.56 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[279, 271, 3963, 3965])).
% 1.34/1.56 tff(3967,plain,
% 1.34/1.56 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[325, 3966])).
% 1.34/1.56 tff(3968,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3969,plain,
% 1.34/1.56 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(3970,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[3969])).
% 1.34/1.56 tff(3971,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[3970, 3968])).
% 1.34/1.56 tff(3972,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(3973,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[3972, 3971])).
% 1.34/1.56 tff(3974,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3973, 77, 3953, 292, 327])).
% 1.34/1.56 tff(3975,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(3976,plain,
% 1.34/1.56 (~r(s(z), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3975, 3967, 3952])).
% 1.34/1.56 tff(3977,plain,
% 1.34/1.56 (b(s(z), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[194, 3976])).
% 1.34/1.56 tff(3978,plain,
% 1.34/1.56 (b(s(z), elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[175, 1662])).
% 1.34/1.56 tff(3979,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[340, 3978])).
% 1.34/1.56 tff(3980,plain,((~(elem!1 = s(s(s(z))))) | b(s(z), elem!1) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(3981,plain,
% 1.34/1.56 (~(elem!1 = s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3980, 3977, 340])).
% 1.34/1.56 tff(3982,plain,
% 1.34/1.56 (~r(s(s(z)), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[96, 77, 67, 26])).
% 1.34/1.56 tff(3983,plain,
% 1.34/1.56 (b(s(s(z)), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[105, 3982])).
% 1.34/1.56 tff(3984,plain,
% 1.34/1.56 (~r(s(s(s(z))), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[85, 67, 26])).
% 1.34/1.56 tff(3985,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[89, 21, 3984, 56])).
% 1.34/1.56 tff(3986,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.56 tff(3987,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3951, 3986])).
% 1.34/1.56 tff(3988,plain,
% 1.34/1.56 (~r(s(z), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[203, 67, 66])).
% 1.34/1.56 tff(3989,plain,
% 1.34/1.56 (b(s(z), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[210, 3988])).
% 1.34/1.56 tff(3990,plain,
% 1.34/1.56 (~r(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3961, 67, 3987])).
% 1.34/1.56 tff(3991,plain,
% 1.34/1.56 (b(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[247, 3990])).
% 1.34/1.56 tff(3992,plain,
% 1.34/1.56 (~b(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[279, 271, 3991, 3989])).
% 1.34/1.56 tff(3993,plain,
% 1.34/1.56 (r(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[325, 3992])).
% 1.34/1.56 tff(3994,plain,
% 1.34/1.56 (~r(s(z), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3975, 3993, 3987])).
% 1.34/1.56 tff(3995,plain,
% 1.34/1.56 (b(s(z), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[194, 3994])).
% 1.34/1.56 tff(3996,plain,
% 1.34/1.56 (~(elem!1 = s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[3980, 3995, 340])).
% 1.34/1.56 tff(3997,plain,
% 1.34/1.56 (~b(s(z), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[184, 3995, 154, 152])).
% 1.34/1.56 tff(3998,plain,
% 1.34/1.56 (r(s(z), s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[172, 3997])).
% 1.34/1.56 tff(3999,plain,
% 1.34/1.56 (~(s(z) = elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1458, 1455, 3989])).
% 1.34/1.56 tff(4000,plain,
% 1.34/1.56 (r(s(z), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[357, 3999, 340])).
% 1.34/1.56 tff(4001,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4002,plain,
% 1.34/1.56 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(4003,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[4002])).
% 1.34/1.56 tff(4004,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[4003, 4001])).
% 1.34/1.56 tff(4005,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(4006,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[4005, 4004])).
% 1.34/1.56 tff(4007,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[4006, 77, 360, 428, 156])).
% 1.34/1.56 tff(4008,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4009,plain,
% 1.34/1.57 (~r(s(s(z)), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4008, 4000, 3998])).
% 1.34/1.57 tff(4010,plain,
% 1.34/1.57 (s(s(z)) = elem!1),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[426, 1, 4009])).
% 1.34/1.57 tff(4011,plain,
% 1.34/1.57 (s(s(s(z))) = s(elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4010])).
% 1.34/1.57 tff(4012,plain,
% 1.34/1.57 (s(elem!1) = s(s(s(z)))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4011])).
% 1.34/1.57 tff(4013,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4012])).
% 1.34/1.57 tff(4014,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4013])).
% 1.34/1.57 tff(4015,plain,
% 1.34/1.57 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4012])).
% 1.34/1.57 tff(4016,plain,
% 1.34/1.57 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4015])).
% 1.34/1.57 tff(4017,plain,
% 1.34/1.57 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4012])).
% 1.34/1.57 tff(4018,plain,
% 1.34/1.57 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4017])).
% 1.34/1.57 tff(4019,plain,
% 1.34/1.57 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4010])).
% 1.34/1.57 tff(4020,plain,
% 1.34/1.57 (b(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[152, 4019])).
% 1.34/1.57 tff(4021,plain,
% 1.34/1.57 (b(elem!1, s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4020, 4018])).
% 1.34/1.57 tff(4022,plain,
% 1.34/1.57 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4012])).
% 1.34/1.57 tff(4023,plain,
% 1.34/1.57 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4022])).
% 1.34/1.57 tff(4024,plain,
% 1.34/1.57 (b(s(z), s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[3995, 4023])).
% 1.34/1.57 tff(4025,plain,
% 1.34/1.57 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4012])).
% 1.34/1.57 tff(4026,plain,
% 1.34/1.57 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[4025])).
% 1.34/1.57 tff(4027,plain,
% 1.34/1.57 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4010])).
% 1.34/1.57 tff(4028,plain,
% 1.34/1.57 (b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[154, 4027])).
% 1.34/1.57 tff(4029,plain,
% 1.34/1.57 (b(s(elem!1), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4028, 4026])).
% 1.34/1.57 tff(4030,plain,
% 1.34/1.57 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4011])).
% 1.34/1.57 tff(4031,plain,
% 1.34/1.57 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4030])).
% 1.34/1.57 tff(4032,plain,
% 1.34/1.57 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4031])).
% 1.34/1.57 tff(4033,plain,
% 1.34/1.57 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4032])).
% 1.34/1.57 tff(4034,plain,
% 1.34/1.57 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4010])).
% 1.34/1.57 tff(4035,plain,
% 1.34/1.57 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[336, 3998, 3993])).
% 1.34/1.57 tff(4036,plain,
% 1.34/1.57 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[149, 4035])).
% 1.34/1.57 tff(4037,plain,
% 1.34/1.57 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4036, 4034])).
% 1.34/1.57 tff(4038,plain,
% 1.34/1.57 (b(elem!1, s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4037, 4033])).
% 1.34/1.57 tff(4039,plain,
% 1.34/1.57 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[568, 4010])).
% 1.34/1.57 tff(4040,assumption,(b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4041,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4042,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4043,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4044,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4043, 4042])).
% 1.34/1.57 tff(4045,plain,
% 1.34/1.57 ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4044, 116, 1879, 846, 4041])).
% 1.34/1.57 tff(4046,plain,
% 1.34/1.57 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4045, 4040])).
% 1.34/1.57 tff(4047,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[885, 4046, 952])).
% 1.34/1.57 tff(4048,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4049,plain,
% 1.34/1.57 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4050,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4049])).
% 1.34/1.57 tff(4051,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4050, 4048])).
% 1.34/1.57 tff(4052,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4053,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4052, 4051])).
% 1.34/1.57 tff(4054,plain,
% 1.34/1.57 (~r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4053, 77, 360, 4047])).
% 1.34/1.57 tff(4055,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.34/1.57 tff(4056,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4057,plain,
% 1.34/1.57 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4058,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4057])).
% 1.34/1.57 tff(4059,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4058, 4056])).
% 1.34/1.57 tff(4060,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4061,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 1.34/1.57 tff(4062,plain,
% 1.34/1.57 ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4061, 116, 1879, 846, 4055])).
% 1.34/1.57 tff(4063,plain,
% 1.34/1.57 (~b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4062, 4040])).
% 1.34/1.57 tff(4064,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[870, 21, 1901, 4063, 4054])).
% 1.34/1.57 tff(4065,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4066,plain,
% 1.34/1.57 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4065, 4039, 4000, 4038, 4029, 4024, 4021])).
% 1.34/1.57 tff(4067,plain,
% 1.34/1.57 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4066, 4016])).
% 1.34/1.57 tff(4068,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)],[1380, 4067])).
% 1.34/1.57 tff(4069,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4068, 4014])).
% 1.34/1.57 tff(4070,plain,
% 1.34/1.57 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.34/1.57 inference(commutativity,[status(thm)],[])).
% 1.34/1.57 tff(4071,plain,
% 1.34/1.57 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4070])).
% 1.34/1.57 tff(4072,plain,
% 1.34/1.57 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4071])).
% 1.34/1.57 tff(4073,plain,
% 1.34/1.57 (~(z = s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[564, 4072])).
% 1.34/1.57 tff(4074,plain,
% 1.34/1.57 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4031])).
% 1.34/1.57 tff(4075,plain,
% 1.34/1.57 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4074])).
% 1.34/1.57 tff(4076,plain,
% 1.34/1.57 (r(s(z), s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[3993, 4075])).
% 1.34/1.57 tff(4077,plain,
% 1.34/1.57 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4011])).
% 1.34/1.57 tff(4078,plain,
% 1.34/1.57 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[608, 4010])).
% 1.34/1.57 tff(4079,plain,
% 1.34/1.57 (~(elem!1 = z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[409, 3989, 340])).
% 1.34/1.57 tff(4080,plain,
% 1.34/1.57 (~(z = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[445, 4079])).
% 1.34/1.57 tff(4081,plain,
% 1.34/1.57 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[529, 4010, 4080])).
% 1.34/1.57 tff(4082,plain,
% 1.34/1.57 (r(elem!1, z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[545, 1455, 4079])).
% 1.34/1.57 tff(4083,plain,
% 1.34/1.57 (~r(s(s(z)), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1319, 77, 4082, 66])).
% 1.34/1.57 tff(4084,plain,
% 1.34/1.57 (s(s(z)) = elem!1),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[426, 4083, 1])).
% 1.34/1.57 tff(4085,plain,
% 1.34/1.57 (s(s(s(z))) = s(elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4084])).
% 1.34/1.57 tff(4086,plain,
% 1.34/1.57 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4085])).
% 1.34/1.57 tff(4087,plain,
% 1.34/1.57 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4086])).
% 1.34/1.57 tff(4088,plain,
% 1.34/1.57 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4087])).
% 1.34/1.57 tff(4089,plain,
% 1.34/1.57 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4088])).
% 1.34/1.57 tff(4090,plain,
% 1.34/1.57 (r(s(z), s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[327, 4089])).
% 1.34/1.57 tff(4091,plain,
% 1.34/1.57 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4087])).
% 1.34/1.57 tff(4092,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[4091])).
% 1.34/1.57 tff(4093,plain,
% 1.34/1.57 (~r(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2162, 77, 4082, 67])).
% 1.34/1.57 tff(4094,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.34/1.57 tff(4095,plain,
% 1.34/1.57 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1581])).
% 1.34/1.57 tff(4096,plain,
% 1.34/1.57 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4095])).
% 1.34/1.57 tff(4097,plain,
% 1.34/1.57 (~b(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[3986, 4096])).
% 1.34/1.57 tff(4098,plain,
% 1.34/1.57 (elem!1 = s(s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1345, 4097, 4094])).
% 1.34/1.57 tff(4099,plain,
% 1.34/1.57 (s(s(s(z))) = elem!1),
% 1.34/1.57 inference(symmetry,[status(thm)],[4098])).
% 1.34/1.57 tff(4100,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1581])).
% 1.34/1.57 tff(4101,plain,
% 1.34/1.57 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[4100])).
% 1.34/1.57 tff(4102,plain,
% 1.34/1.57 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4101])).
% 1.34/1.57 tff(4103,plain,
% 1.34/1.57 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4094, 4102])).
% 1.34/1.57 tff(4104,plain,
% 1.34/1.57 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[3950, 4103, 3986])).
% 1.34/1.57 tff(4105,plain,
% 1.34/1.57 (s(s(z)) = s(s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[605, 4104])).
% 1.34/1.57 tff(4106,plain,
% 1.34/1.57 (s(s(z)) = elem!1),
% 1.34/1.57 inference(transitivity,[status(thm)],[4105, 4099])).
% 1.34/1.57 tff(4107,plain,
% 1.34/1.57 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.34/1.57 inference(commutativity,[status(thm)],[])).
% 1.34/1.57 tff(4108,plain,
% 1.34/1.57 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1581])).
% 1.34/1.57 tff(4109,plain,
% 1.34/1.57 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.34/1.57 inference(transitivity,[status(thm)],[4108, 4107])).
% 1.34/1.57 tff(4110,plain,
% 1.34/1.57 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4109])).
% 1.34/1.57 tff(4111,plain,
% 1.34/1.57 (~(s(s(z)) = elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[137, 4110])).
% 1.34/1.57 tff(4112,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4111, 4106])).
% 1.34/1.57 tff(4113,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(s(s(s(z)))), s(s(s(z)))) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4114,plain,
% 1.34/1.57 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4113, 4093, 3986])).
% 1.34/1.57 tff(4115,plain,
% 1.34/1.57 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4084])).
% 1.34/1.57 tff(4116,plain,
% 1.34/1.57 (~b(s(z), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[376, 4084, 340])).
% 1.34/1.57 tff(4117,plain,
% 1.34/1.57 (r(s(z), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[172, 4116])).
% 1.34/1.57 tff(4118,plain,
% 1.34/1.57 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[336, 4117, 327])).
% 1.34/1.57 tff(4119,plain,
% 1.34/1.57 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[149, 4118])).
% 1.34/1.57 tff(4120,plain,
% 1.34/1.57 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4119, 4115])).
% 1.34/1.57 tff(4121,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4122,plain,
% 1.34/1.57 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4123,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4122])).
% 1.34/1.57 tff(4124,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4123, 4121])).
% 1.34/1.57 tff(4125,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4126,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4125, 4124])).
% 1.34/1.57 tff(4127,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4126, 116, 1055, 1054, 254, 1725])).
% 1.34/1.57 tff(4128,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4129,plain,
% 1.34/1.57 (~b(s(s(s(s(z)))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4128, 4120, 1055, 3991])).
% 1.34/1.57 tff(4130,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1596, 4129, 4114])).
% 1.34/1.57 tff(4131,plain,
% 1.34/1.57 (r(s(s(elem!1)), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4130, 4092])).
% 1.34/1.57 tff(4132,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4133,plain,
% 1.34/1.57 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4134,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4133])).
% 1.34/1.57 tff(4135,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4134, 4132])).
% 1.34/1.57 tff(4136,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4137,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4136, 4135])).
% 1.34/1.57 tff(4138,plain,
% 1.34/1.57 (~r(s(z), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4137, 77, 4131, 4000])).
% 1.34/1.57 tff(4139,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4138, 4090])).
% 1.34/1.57 tff(4140,plain,(b(elem!1, z) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, elem!1)) | b(s(z), elem!1) | b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(z)), elem!1) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4141,plain,
% 1.34/1.57 (~b(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4140, 1, 3993, 340, 3986, 1455, 67, 66])).
% 1.34/1.57 tff(4142,plain,
% 1.34/1.57 (r(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1044, 4141, 4080])).
% 1.34/1.57 tff(4143,plain,
% 1.34/1.57 (~r(s(s(elem!1)), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1446, 4142, 4000, 3989])).
% 1.34/1.57 tff(4144,plain,
% 1.34/1.57 (b(s(s(elem!1)), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[743, 4143, 4081])).
% 1.34/1.57 tff(4145,plain,
% 1.34/1.57 (~b(s(elem!1), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[3388, 116, 4144, 4038, 4029])).
% 1.34/1.57 tff(4146,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.57 tff(4147,plain,
% 1.34/1.57 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4146, 610])).
% 1.34/1.57 tff(4148,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.57 tff(4149,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4148, 4147])).
% 1.34/1.57 tff(4150,plain,((~b(s(s(s(z))), s(s(elem!1)))) | b(s(elem!1), s(s(elem!1))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(4151,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4150, 4145, 4010])).
% 1.34/1.57 tff(4152,plain,
% 1.34/1.57 (r(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[664, 4151, 4078])).
% 1.34/1.57 tff(4153,plain,
% 1.34/1.57 (r(s(elem!1), s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4152, 4077])).
% 1.34/1.57 tff(4154,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4155,plain,
% 1.34/1.57 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4156,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[4155])).
% 1.34/1.57 tff(4157,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[4156, 4154])).
% 1.34/1.57 tff(4158,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(4159,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[4158, 4157])).
% 1.34/1.57 tff(4160,plain,
% 1.34/1.57 ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4159, 77, 4000, 4153])).
% 1.34/1.57 tff(4161,plain,
% 1.34/1.57 (~r(s(elem!1), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[4160, 4076])).
% 1.34/1.57 tff(4162,plain,
% 1.34/1.57 (~(s(elem!1) = s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[842, 4010])).
% 1.34/1.57 tff(4163,plain,
% 1.34/1.57 (b(s(elem!1), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[735, 21, 4162, 4161])).
% 1.34/1.57 tff(4164,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4165,plain,
% 1.34/1.57 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(4166,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4165])).
% 1.34/1.58 tff(4167,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4166, 4164])).
% 1.34/1.58 tff(4168,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4169,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4168, 4167])).
% 1.34/1.58 tff(4170,plain,
% 1.34/1.58 (~b(z, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4169, 116, 3989, 271, 4163])).
% 1.34/1.58 tff(4171,plain,
% 1.34/1.58 (((~![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)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4172,plain,
% 1.34/1.58 ((~![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)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4173,plain,
% 1.34/1.58 ((~![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))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4172, 4171])).
% 1.34/1.58 tff(4174,plain,
% 1.34/1.58 ((z = s(elem!1)) | r(z, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4173, 21, 4170])).
% 1.34/1.58 tff(4175,plain,
% 1.34/1.58 (r(z, s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4174, 4073])).
% 1.34/1.58 tff(4176,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4177,plain,
% 1.34/1.58 (((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4178,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4177])).
% 1.34/1.58 tff(4179,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4178, 4176])).
% 1.34/1.58 tff(4180,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4181,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4180, 4179])).
% 1.34/1.58 tff(4182,plain,
% 1.34/1.58 ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4181, 77, 4142, 4175])).
% 1.34/1.58 tff(4183,plain,
% 1.34/1.58 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4182, 4069])).
% 1.34/1.58 tff(4184,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4030])).
% 1.34/1.58 tff(4185,plain,
% 1.34/1.58 (b(s(s(elem!1)), z)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[3991, 4184])).
% 1.34/1.58 tff(4186,plain,
% 1.34/1.58 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[912, 4010])).
% 1.34/1.58 tff(4187,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4030, 4011])).
% 1.34/1.58 tff(4188,plain,
% 1.34/1.58 (r(s(s(elem!1)), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[3987, 4187])).
% 1.34/1.58 tff(4189,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4190,plain,
% 1.34/1.58 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4191,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4190])).
% 1.34/1.58 tff(4192,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4191, 4189])).
% 1.34/1.58 tff(4193,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4194,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4193, 4192])).
% 1.34/1.58 tff(4195,plain,
% 1.34/1.58 (~r(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4194, 77, 4188, 4175])).
% 1.34/1.58 tff(4196,plain,
% 1.34/1.58 (b(z, s(s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[514, 4195])).
% 1.34/1.58 tff(4197,plain,
% 1.34/1.58 (~b(s(s(s(s(s(z))))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[986, 4196, 3989, 1901, 4186, 4144, 4185])).
% 1.34/1.58 tff(4198,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[898, 21, 895, 4197, 4183])).
% 1.34/1.58 tff(4199,plain,(b(s(s(z)), elem!1) | (~b(z, s(z))) | b(s(z), elem!1) | b(s(s(s(s(z)))), s(s(s(z)))) | b(elem!1, z) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4200,plain,
% 1.34/1.58 (b(s(s(z)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4199, 1455, 340, 3986, 271, 67, 66])).
% 1.34/1.58 tff(4201,plain,
% 1.34/1.58 (~b(elem!1, s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1340, 4200, 154, 152])).
% 1.34/1.58 tff(4202,plain,
% 1.34/1.58 (r(elem!1, s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1345, 4201, 3996])).
% 1.34/1.58 tff(4203,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2162, 77, 4082, 67, 4202])).
% 1.34/1.58 tff(4204,plain,(b(elem!1, z) | (~r(s(s(s(z))), z)) | b(s(z), elem!1) | b(s(s(s(s(z)))), s(s(s(z)))) | (~b(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4205,plain,
% 1.34/1.58 (b(elem!1, z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4204, 271, 340, 3946, 67, 26])).
% 1.34/1.58 tff(4206,plain,
% 1.34/1.58 (~(s(s(z)) = elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[540, 4205, 2])).
% 1.34/1.58 tff(4207,plain,
% 1.34/1.58 (~b(s(z), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[184, 3977, 3985, 3983])).
% 1.34/1.58 tff(4208,plain,
% 1.34/1.58 (r(s(z), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[172, 4207])).
% 1.34/1.58 tff(4209,plain,
% 1.34/1.58 (~r(z, elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[456, 428, 66])).
% 1.34/1.58 tff(4210,plain,
% 1.34/1.58 (b(z, elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1044, 4209, 4080])).
% 1.34/1.58 tff(4211,plain,
% 1.34/1.58 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(4212,plain,
% 1.34/1.58 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4211])).
% 1.34/1.58 tff(4213,plain,
% 1.34/1.58 ((~(s(elem!1) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4212])).
% 1.34/1.58 tff(4214,plain,
% 1.34/1.58 (~r(s(z), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4008, 156, 428])).
% 1.34/1.58 tff(4215,plain,
% 1.34/1.58 (s(z) = elem!1),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[357, 4214, 340])).
% 1.34/1.58 tff(4216,plain,
% 1.34/1.58 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1531, 4215])).
% 1.34/1.58 tff(4217,plain,
% 1.34/1.58 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1364, 4216])).
% 1.34/1.58 tff(4218,plain,
% 1.34/1.58 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4217, 4213])).
% 1.34/1.58 tff(4219,plain,
% 1.34/1.58 (s(s(z)) = s(elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4215])).
% 1.34/1.58 tff(4220,plain,
% 1.34/1.58 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4219])).
% 1.34/1.58 tff(4221,plain,
% 1.34/1.58 (r(s(elem!1), elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[428, 4220])).
% 1.34/1.58 tff(4222,plain,
% 1.34/1.58 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(4223,plain,
% 1.34/1.58 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4215])).
% 1.34/1.58 tff(4224,plain,
% 1.34/1.58 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.58 inference(transitivity,[status(thm)],[4223, 4222])).
% 1.34/1.58 tff(4225,plain,
% 1.34/1.58 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4224])).
% 1.34/1.58 tff(4226,plain,
% 1.34/1.58 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1901, 4225])).
% 1.34/1.58 tff(4227,plain,
% 1.34/1.58 (s(s(s(z))) = s(s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4219])).
% 1.34/1.58 tff(4228,plain,
% 1.34/1.58 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4227])).
% 1.34/1.58 tff(4229,plain,
% 1.34/1.58 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4228, 1504])).
% 1.34/1.58 tff(4230,plain,
% 1.34/1.58 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4229])).
% 1.34/1.58 tff(4231,plain,
% 1.34/1.58 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1138, 4230])).
% 1.34/1.58 tff(4232,plain,
% 1.34/1.58 (r(s(s(elem!1)), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1482, 4215, 67])).
% 1.34/1.58 tff(4233,plain,
% 1.34/1.58 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4215])).
% 1.34/1.58 tff(4234,plain,
% 1.34/1.58 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4233])).
% 1.34/1.58 tff(4235,plain,
% 1.34/1.58 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[566, 4234])).
% 1.34/1.58 tff(4236,plain,
% 1.34/1.58 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4227])).
% 1.34/1.58 tff(4237,plain,
% 1.34/1.58 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4236])).
% 1.34/1.58 tff(4238,plain,
% 1.34/1.58 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4237])).
% 1.34/1.58 tff(4239,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4227])).
% 1.34/1.58 tff(4240,plain,
% 1.34/1.58 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4239])).
% 1.34/1.58 tff(4241,plain,
% 1.34/1.58 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4240])).
% 1.34/1.58 tff(4242,plain,
% 1.34/1.58 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4236])).
% 1.34/1.58 tff(4243,plain,
% 1.34/1.58 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4242])).
% 1.34/1.58 tff(4244,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4219])).
% 1.34/1.58 tff(4245,plain,
% 1.34/1.58 (b(s(s(s(z))), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[154, 4244])).
% 1.34/1.58 tff(4246,plain,
% 1.34/1.58 (b(s(s(elem!1)), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4245, 4243])).
% 1.34/1.58 tff(4247,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4219])).
% 1.34/1.58 tff(4248,plain,
% 1.34/1.58 (r(elem!1, s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2959, 4215, 156])).
% 1.34/1.58 tff(4249,plain,
% 1.34/1.58 (r(elem!1, s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1068, 4216, 1525])).
% 1.34/1.58 tff(4250,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.34/1.58 tff(4251,plain,
% 1.34/1.58 (r(elem!1, s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4250, 2952])).
% 1.34/1.58 tff(4252,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1512])).
% 1.34/1.58 tff(4253,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[4252])).
% 1.34/1.58 tff(4254,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[229, 4253])).
% 1.34/1.58 tff(4255,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4256,plain,
% 1.34/1.58 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4257,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4256])).
% 1.34/1.58 tff(4258,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4257, 4255])).
% 1.34/1.58 tff(4259,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4260,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4259, 4258])).
% 1.34/1.58 tff(4261,plain,
% 1.34/1.58 ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4260, 77, 429])).
% 1.34/1.58 tff(4262,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4261, 4254, 4251])).
% 1.34/1.58 tff(4263,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(4264,plain,
% 1.34/1.58 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4263, 4249, 4215, 4248])).
% 1.34/1.58 tff(4265,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[226, 4264])).
% 1.34/1.58 tff(4266,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4265, 4247])).
% 1.34/1.58 tff(4267,plain,
% 1.34/1.58 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4219, 4227])).
% 1.34/1.58 tff(4268,plain,
% 1.34/1.58 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[152, 4267])).
% 1.34/1.58 tff(4269,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4270,plain,
% 1.34/1.58 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4271,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4270])).
% 1.34/1.58 tff(4272,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4271, 4269])).
% 1.34/1.58 tff(4273,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4274,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 1.34/1.58 tff(4275,plain,
% 1.34/1.58 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4274, 116, 4268, 4266, 4246])).
% 1.34/1.58 tff(4276,plain,
% 1.34/1.58 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4275, 4241])).
% 1.34/1.58 tff(4277,plain,
% 1.34/1.58 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1146, 4276])).
% 1.34/1.58 tff(4278,plain,
% 1.34/1.58 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4277, 4238])).
% 1.34/1.58 tff(4279,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4280,plain,
% 1.34/1.58 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4281,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[4280])).
% 1.34/1.58 tff(4282,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[4281, 4279])).
% 1.34/1.58 tff(4283,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(4284,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[4283, 4282])).
% 1.34/1.58 tff(4285,plain,
% 1.34/1.58 (~r(s(s(elem!1)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[4284, 77, 4249, 4278])).
% 1.34/1.58 tff(4286,plain,
% 1.34/1.58 (b(s(s(elem!1)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[743, 4285, 4235])).
% 1.34/1.58 tff(4287,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(4288,plain,
% 1.34/1.58 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4289,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4288])).
% 1.34/1.59 tff(4290,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4289, 4287])).
% 1.34/1.59 tff(4291,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4292,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4291, 4290])).
% 1.34/1.59 tff(4293,plain,
% 1.34/1.59 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4292, 116, 1055, 537, 616, 845])).
% 1.34/1.59 tff(4294,plain,
% 1.34/1.59 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[916, 21, 953, 4293])).
% 1.34/1.59 tff(4295,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4296,plain,
% 1.34/1.59 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4297,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4296])).
% 1.34/1.59 tff(4298,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4297, 4295])).
% 1.34/1.59 tff(4299,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4300,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4299, 4298])).
% 1.34/1.59 tff(4301,plain,
% 1.34/1.59 (~b(s(s(s(s(s(z))))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4300, 116, 1055, 537, 845])).
% 1.34/1.59 tff(4302,plain,
% 1.34/1.59 (r(s(s(s(s(s(z))))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[898, 21, 895, 4301])).
% 1.34/1.59 tff(4303,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4304,plain,
% 1.34/1.59 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4305,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4304])).
% 1.34/1.59 tff(4306,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4305, 4303])).
% 1.34/1.59 tff(4307,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4308,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4307, 4306])).
% 1.34/1.59 tff(4309,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4308, 77, 3208, 4302, 4294])).
% 1.34/1.59 tff(4310,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(4311,plain,
% 1.34/1.59 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4310, 4286, 1055, 4232, 537, 4231])).
% 1.34/1.59 tff(4312,plain,
% 1.34/1.59 (r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[885, 4311, 4226])).
% 1.34/1.59 tff(4313,plain,
% 1.34/1.59 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4219])).
% 1.34/1.59 tff(4314,plain,
% 1.34/1.59 (r(s(elem!1), z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[66, 4313])).
% 1.34/1.59 tff(4315,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4316,plain,
% 1.34/1.59 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4317,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4316])).
% 1.34/1.59 tff(4318,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4317, 4315])).
% 1.34/1.59 tff(4319,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4320,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4319, 4318])).
% 1.34/1.59 tff(4321,plain,
% 1.34/1.59 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4320, 77, 4314, 4312, 4221])).
% 1.34/1.59 tff(4322,plain,
% 1.34/1.59 (((~![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)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4323,plain,
% 1.34/1.59 ((~![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)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4324,plain,
% 1.34/1.59 ((~![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))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4323, 4322])).
% 1.34/1.59 tff(4325,plain,
% 1.34/1.59 ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4324, 21, 4321])).
% 1.34/1.59 tff(4326,plain,
% 1.34/1.59 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4325, 4218])).
% 1.34/1.59 tff(4327,plain,
% 1.34/1.59 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1584, 4216])).
% 1.34/1.59 tff(4328,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1475])).
% 1.34/1.59 tff(4329,plain,
% 1.34/1.59 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[600])).
% 1.34/1.59 tff(4330,plain,
% 1.34/1.59 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4329, 138])).
% 1.34/1.59 tff(4331,plain,
% 1.34/1.59 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[4330])).
% 1.34/1.59 tff(4332,plain,
% 1.34/1.59 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4331])).
% 1.34/1.59 tff(4333,plain,
% 1.34/1.59 (~(s(s(z)) = s(s(s(z))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[141, 4332])).
% 1.34/1.59 tff(4334,plain,
% 1.34/1.59 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1476, 600])).
% 1.34/1.59 tff(4335,plain,
% 1.34/1.59 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4334])).
% 1.34/1.59 tff(4336,plain,
% 1.34/1.59 (s(s(z)) = s(s(s(z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1474, 561, 4335, 127])).
% 1.34/1.59 tff(4337,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[603, 4336])).
% 1.34/1.59 tff(4338,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (s(s(z)) = s(s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(4339,plain,
% 1.34/1.59 (s(s(z)) = s(s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4338, 599, 466])).
% 1.34/1.59 tff(4340,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4339, 4333])).
% 1.34/1.59 tff(4341,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (s(s(s(s(z)))) = s(s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(4342,plain,
% 1.34/1.59 ((~(s(s(s(s(z)))) = s(s(s(z))))) | (~(s(z) = elem!1))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4341, 137])).
% 1.34/1.59 tff(4343,plain,
% 1.34/1.59 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4342, 466])).
% 1.34/1.59 tff(4344,plain,
% 1.34/1.59 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2012])).
% 1.34/1.59 tff(4345,plain,
% 1.34/1.59 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4344])).
% 1.34/1.59 tff(4346,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4347,plain,
% 1.34/1.59 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4348,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4347])).
% 1.34/1.59 tff(4349,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4348, 4346])).
% 1.34/1.59 tff(4350,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4351,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4350, 4349])).
% 1.34/1.59 tff(4352,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4351, 116, 1055, 537, 616, 1725])).
% 1.34/1.59 tff(4353,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4352, 4345])).
% 1.34/1.59 tff(4354,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[3950, 4353, 4343])).
% 1.34/1.59 tff(4355,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4354, 4328])).
% 1.34/1.59 tff(4356,plain,
% 1.34/1.59 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4357,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4356])).
% 1.34/1.59 tff(4358,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4357, 1586])).
% 1.34/1.59 tff(4359,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4360,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4359, 4358])).
% 1.34/1.59 tff(4361,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4360, 116, 1055, 537, 1725])).
% 1.34/1.59 tff(4362,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[247, 4361])).
% 1.34/1.59 tff(4363,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4364,plain,
% 1.34/1.59 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4365,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4364])).
% 1.34/1.59 tff(4366,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4365, 4363])).
% 1.34/1.59 tff(4367,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4368,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4367, 4366])).
% 1.34/1.59 tff(4369,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4368, 77, 3208, 4362, 4355])).
% 1.34/1.59 tff(4370,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), z)) | (~(s(z) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(4371,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[4370, 4286, 1055, 537, 4215, 4232])).
% 1.34/1.59 tff(4372,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1596, 4371, 4327])).
% 1.34/1.59 tff(4373,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4374,plain,
% 1.34/1.59 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(4375,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[4374])).
% 1.34/1.59 tff(4376,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[4375, 4373])).
% 1.34/1.59 tff(4377,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(4378,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[4377, 4376])).
% 1.34/1.60 tff(4379,plain,
% 1.34/1.60 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[4378, 77, 4372, 4312])).
% 1.34/1.60 tff(4380,plain,
% 1.34/1.60 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1940, 21, 1708, 4379])).
% 1.34/1.60 tff(4381,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(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))))))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(4382,plain,
% 1.34/1.60 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~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))))))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(4383,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(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)))))))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[4382])).
% 1.34/1.60 tff(4384,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(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))))))))),
% 1.34/1.60 inference(transitivity,[status(thm)],[4383, 4381])).
% 1.34/1.60 tff(4385,plain,
% 1.34/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(4386,plain,
% 1.34/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[4385, 4384])).
% 1.34/1.60 tff(4387,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[4386, 116, 4286, 4268, 4266, 4380, 4326])).
% 1.34/1.60 tff(4388,plain,((~r(s(z), s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | b(elem!1, s(s(s(s(z))))) | (~r(s(s(s(z))), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(4389,plain,
% 1.34/1.60 (b(elem!1, s(s(s(s(z)))))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[4388, 4210, 156, 537, 66, 428, 67, 340])).
% 1.34/1.60 tff(4390,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1063, 4389, 4210, 537, 254])).
% 1.34/1.60 tff(4391,plain,((~r(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(4392,plain,
% 1.44/1.60 (~r(s(s(z)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4391, 4205, 3963, 4208, 26, 67, 340])).
% 1.44/1.60 tff(4393,plain,
% 1.44/1.60 (b(s(s(z)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[426, 4392, 4206])).
% 1.44/1.60 tff(4394,plain,
% 1.44/1.60 (~b(elem!1, s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1340, 4393, 3985, 3983])).
% 1.44/1.60 tff(4395,plain,
% 1.44/1.60 (r(elem!1, s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1345, 4394, 3981])).
% 1.44/1.60 tff(4396,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4397,plain,
% 1.44/1.60 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4398,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4397])).
% 1.44/1.60 tff(4399,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[4398, 4396])).
% 1.44/1.60 tff(4400,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(4401,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[4400, 4399])).
% 1.44/1.60 tff(4402,plain,
% 1.44/1.60 (~r(elem!1, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4401, 77, 3952, 4395])).
% 1.44/1.60 tff(4403,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4404,plain,
% 1.44/1.60 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4405,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4404])).
% 1.44/1.60 tff(4406,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[4405, 4403])).
% 1.44/1.60 tff(4407,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(4408,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[4407, 4406])).
% 1.44/1.60 tff(4409,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4408, 77, 3952, 4395])).
% 1.44/1.60 tff(4410,plain,
% 1.44/1.60 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[336, 4208, 3967])).
% 1.44/1.60 tff(4411,plain,
% 1.44/1.60 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[149, 4410])).
% 1.44/1.60 tff(4412,plain,
% 1.44/1.60 (b(elem!1, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1068, 1362, 1049])).
% 1.44/1.60 tff(4413,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1596, 2416, 3289])).
% 1.44/1.60 tff(4414,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2431, 4413, 4412, 1331, 2410])).
% 1.44/1.60 tff(4415,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(4416,plain,
% 1.44/1.60 (elem!1 = s(s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4415, 4393, 4411, 4409, 4402])).
% 1.44/1.60 tff(4417,plain,
% 1.44/1.60 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4416])).
% 1.44/1.60 tff(4418,plain,
% 1.44/1.60 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4417])).
% 1.44/1.60 tff(4419,plain,
% 1.44/1.60 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.44/1.60 inference(symmetry,[status(thm)],[4418])).
% 1.44/1.60 tff(4420,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4419])).
% 1.44/1.60 tff(4421,plain,
% 1.44/1.60 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.60 inference(symmetry,[status(thm)],[4420])).
% 1.44/1.60 tff(4422,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4423,plain,
% 1.44/1.60 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4424,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4423])).
% 1.44/1.60 tff(4425,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[4424, 4422])).
% 1.44/1.60 tff(4426,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(4427,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[4426, 4425])).
% 1.44/1.60 tff(4428,plain,
% 1.44/1.60 (~b(s(s(z)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4427, 116, 3983, 3985, 3977])).
% 1.44/1.60 tff(4429,plain,
% 1.44/1.60 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[466])).
% 1.44/1.60 tff(4430,plain,
% 1.44/1.60 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.44/1.60 inference(symmetry,[status(thm)],[4429])).
% 1.44/1.60 tff(4431,plain,
% 1.44/1.60 (b(s(s(z)), s(z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[1331, 4430])).
% 1.44/1.60 tff(4432,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.44/1.60 tff(4433,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4432, 4431])).
% 1.44/1.60 tff(4434,plain,((~(s(z) = elem!1)) | b(s(s(z)), s(z)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(4435,plain,
% 1.44/1.60 (~(s(z) = elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4434, 4393, 4428])).
% 1.44/1.60 tff(4436,plain,
% 1.44/1.60 (r(s(z), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[357, 4435, 340])).
% 1.44/1.60 tff(4437,plain,
% 1.44/1.60 (~(elem!1 = s(s(elem!1)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1090, 4416])).
% 1.44/1.60 tff(4438,plain,
% 1.44/1.60 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1097, 4437])).
% 1.44/1.60 tff(4439,plain,
% 1.44/1.60 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4416])).
% 1.44/1.60 tff(4440,plain,
% 1.44/1.60 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(symmetry,[status(thm)],[4439])).
% 1.44/1.60 tff(4441,plain,
% 1.44/1.60 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4418])).
% 1.44/1.60 tff(4442,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.60 inference(symmetry,[status(thm)],[4441])).
% 1.44/1.60 tff(4443,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), elem!1)),
% 1.44/1.60 inference(transitivity,[status(thm)],[4442, 4440])).
% 1.44/1.60 tff(4444,plain,
% 1.44/1.60 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4443])).
% 1.44/1.60 tff(4445,plain,
% 1.44/1.60 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4416])).
% 1.44/1.60 tff(4446,plain,
% 1.44/1.60 (~(elem!1 = z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[409, 3965, 340])).
% 1.44/1.60 tff(4447,plain,
% 1.44/1.60 (~(z = elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[445, 4446])).
% 1.44/1.60 tff(4448,plain,
% 1.44/1.60 (r(s(s(z)), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[391, 21, 4428, 388])).
% 1.44/1.60 tff(4449,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4450,plain,
% 1.44/1.60 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4451,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4450])).
% 1.44/1.60 tff(4452,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[4451, 4449])).
% 1.44/1.60 tff(4453,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(4454,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[4453, 4452])).
% 1.44/1.60 tff(4455,plain,
% 1.44/1.60 (~b(elem!1, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4454, 116, 4205, 3965, 271])).
% 1.44/1.60 tff(4456,plain,
% 1.44/1.60 (~(elem!1 = s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[420, 4435])).
% 1.44/1.60 tff(4457,plain,
% 1.44/1.60 (r(elem!1, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[633, 4456, 4455])).
% 1.44/1.60 tff(4458,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4459,plain,
% 1.44/1.60 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4460,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4459])).
% 1.44/1.60 tff(4461,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[4460, 4458])).
% 1.44/1.60 tff(4462,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(4463,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[4462, 4461])).
% 1.44/1.60 tff(4464,plain,
% 1.44/1.60 (~r(elem!1, s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4463, 77, 4457, 26, 4448])).
% 1.44/1.60 tff(4465,plain,
% 1.44/1.60 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1077])).
% 1.44/1.60 tff(4466,plain,
% 1.44/1.60 (r(z, s(s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[448, 4465])).
% 1.44/1.60 tff(4467,plain,
% 1.44/1.60 (r(elem!1, s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1077])).
% 1.44/1.60 tff(4468,plain,
% 1.44/1.60 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4467])).
% 1.44/1.60 tff(4469,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2956, 4468])).
% 1.44/1.60 tff(4470,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[226, 4469])).
% 1.44/1.60 tff(4471,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4472,plain,
% 1.44/1.60 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(4473,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[4472])).
% 1.44/1.60 tff(4474,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[4473, 4471])).
% 1.44/1.60 tff(4475,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(4476,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[4475, 4474])).
% 1.44/1.60 tff(4477,plain,
% 1.44/1.60 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[4476, 116, 4470, 27, 176])).
% 1.44/1.60 tff(4478,plain,
% 1.44/1.60 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1146, 4477])).
% 1.44/1.60 tff(4479,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4480,plain,
% 1.44/1.61 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4481,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4480])).
% 1.44/1.61 tff(4482,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4481, 4479])).
% 1.44/1.61 tff(4483,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4484,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4483, 4482])).
% 1.44/1.61 tff(4485,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4484, 77, 67, 4478, 4466])).
% 1.44/1.61 tff(4486,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | r(elem!1, s(s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(4487,plain,
% 1.44/1.61 (~r(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4486, 4416, 3983, 3985, 4464, 67])).
% 1.44/1.61 tff(4488,plain,
% 1.44/1.61 (b(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1044, 4487, 4447])).
% 1.44/1.61 tff(4489,plain,
% 1.44/1.61 (b(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4488, 4445])).
% 1.44/1.61 tff(4490,plain,
% 1.44/1.61 (r(elem!1, s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4416])).
% 1.44/1.61 tff(4491,plain,
% 1.44/1.61 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4490])).
% 1.44/1.61 tff(4492,plain,
% 1.44/1.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4464, 4491])).
% 1.44/1.61 tff(4493,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[226, 4492])).
% 1.44/1.61 tff(4494,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4495,plain,
% 1.44/1.61 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4496,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4495])).
% 1.44/1.61 tff(4497,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4496, 4494])).
% 1.44/1.61 tff(4498,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4499,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4498, 4497])).
% 1.44/1.61 tff(4500,plain,
% 1.44/1.61 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4499, 116, 212, 27, 2410, 1181])).
% 1.44/1.61 tff(4501,plain,
% 1.44/1.61 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1279, 21, 1276, 4500])).
% 1.44/1.61 tff(4502,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4503,plain,
% 1.44/1.61 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4504,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4503])).
% 1.44/1.61 tff(4505,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4504, 4502])).
% 1.44/1.61 tff(4506,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4507,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 1.44/1.61 tff(4508,plain,
% 1.44/1.61 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4507, 116, 212, 27, 1176, 1181])).
% 1.44/1.61 tff(4509,plain,
% 1.44/1.61 (r(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1232, 21, 1229, 4508])).
% 1.44/1.61 tff(4510,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4511,plain,
% 1.44/1.61 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4512,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4511])).
% 1.44/1.61 tff(4513,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4512, 4510])).
% 1.44/1.61 tff(4514,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4515,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 1.44/1.61 tff(4516,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4515, 77, 66, 4509, 4501])).
% 1.44/1.61 tff(4517,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(4518,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)],[4517, 4493, 26, 3983, 4411, 4489])).
% 1.44/1.61 tff(4519,plain,
% 1.44/1.61 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4518, 4444])).
% 1.44/1.61 tff(4520,plain,
% 1.44/1.61 (r(s(s(elem!1)), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[743, 4519, 4438])).
% 1.44/1.61 tff(4521,plain,
% 1.44/1.61 (~r(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1245, 4520, 4436])).
% 1.44/1.61 tff(4522,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[808, 4521])).
% 1.44/1.61 tff(4523,plain,
% 1.44/1.61 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4522, 4421])).
% 1.44/1.61 tff(4524,plain,
% 1.44/1.61 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4418, 4416])).
% 1.44/1.61 tff(4525,plain,
% 1.44/1.61 ((~(s(s(elem!1)) = elem!1)) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4524])).
% 1.44/1.61 tff(4526,plain,
% 1.44/1.61 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4438, 4525])).
% 1.44/1.61 tff(4527,plain,
% 1.44/1.61 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1615, 4518, 4526])).
% 1.44/1.61 tff(4528,plain,
% 1.44/1.61 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4476, 116, 4493, 3983, 3985])).
% 1.44/1.61 tff(4529,plain,
% 1.44/1.61 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1146, 4528])).
% 1.44/1.61 tff(4530,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4531,plain,
% 1.44/1.61 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(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(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4532,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4531])).
% 1.44/1.61 tff(4533,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4532, 4530])).
% 1.44/1.61 tff(4534,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4535,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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(z))))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4534, 4533])).
% 1.44/1.61 tff(4536,plain,
% 1.44/1.61 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4535, 77, 4529, 4527])).
% 1.44/1.61 tff(4537,plain,
% 1.44/1.61 (((~![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))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4538,plain,
% 1.44/1.61 ((~![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))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4539,plain,
% 1.44/1.61 ((~![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)))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4538, 4537])).
% 1.44/1.61 tff(4540,plain,
% 1.44/1.61 ((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)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4539, 21])).
% 1.44/1.61 tff(4541,plain,
% 1.44/1.61 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4540, 1204])).
% 1.44/1.61 tff(4542,plain,
% 1.44/1.61 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4541, 4536])).
% 1.44/1.61 tff(4543,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4544,plain,
% 1.44/1.61 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4545,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4544])).
% 1.44/1.61 tff(4546,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4545, 4543])).
% 1.44/1.61 tff(4547,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4548,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4547, 4546])).
% 1.44/1.61 tff(4549,plain,
% 1.44/1.61 (~r(s(s(s(z))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4548, 77, 4529, 4208, 3967])).
% 1.44/1.61 tff(4550,plain,
% 1.44/1.61 (b(s(s(s(z))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[402, 21, 135, 4549])).
% 1.44/1.61 tff(4551,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4552,plain,
% 1.44/1.61 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(4553,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4552])).
% 1.44/1.61 tff(4554,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[4553, 4551])).
% 1.44/1.61 tff(4555,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(4556,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 1.44/1.61 tff(4557,plain,
% 1.44/1.61 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4556, 116, 3965, 271, 4550])).
% 1.44/1.61 tff(4558,plain,
% 1.44/1.61 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4557, 4542])).
% 1.44/1.61 tff(4559,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4558, 4523])).
% 1.44/1.61 tff(4560,plain,((~b(z, s(z))) | (~r(s(s(s(z))), z)) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(4561,plain,
% 1.44/1.61 (~b(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[4560, 64, 340, 2])).
% 1.44/1.61 tff(4562,plain,
% 1.44/1.61 (r(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[289, 4561])).
% 1.44/1.61 tff(4563,plain,
% 1.44/1.61 (~r(s(s(z)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3659, 4562, 26])).
% 1.44/1.61 tff(4564,plain,
% 1.44/1.61 (~r(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3295, 4000, 293])).
% 1.44/1.61 tff(4565,plain,
% 1.44/1.61 (b(z, elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1044, 4564, 4080])).
% 1.44/1.61 tff(4566,plain,
% 1.44/1.61 (~(elem!1 = s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[420, 3999])).
% 1.44/1.61 tff(4567,plain,
% 1.44/1.61 (~r(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2095, 4082, 293])).
% 1.44/1.61 tff(4568,plain,
% 1.44/1.61 (b(elem!1, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[633, 4567, 4566])).
% 1.44/1.61 tff(4569,plain,
% 1.44/1.61 (s(s(z)) = elem!1),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[426, 1, 4083])).
% 1.44/1.61 tff(4570,plain,
% 1.44/1.61 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[568, 4569])).
% 1.44/1.61 tff(4571,plain,
% 1.44/1.61 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3195, 1055, 3989, 667])).
% 1.44/1.61 tff(4572,plain,
% 1.44/1.61 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[529, 4569, 4080])).
% 1.44/1.61 tff(4573,plain,
% 1.44/1.61 (r(s(s(elem!1)), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[743, 4572, 4571])).
% 1.44/1.61 tff(4574,plain,
% 1.44/1.61 (~r(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1245, 4573, 4000])).
% 1.44/1.61 tff(4575,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[808, 4574])).
% 1.44/1.61 tff(4576,plain,
% 1.44/1.61 (s(s(s(z))) = s(elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4569])).
% 1.44/1.61 tff(4577,plain,
% 1.44/1.61 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[4576])).
% 1.44/1.61 tff(4578,plain,
% 1.44/1.61 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4577])).
% 1.44/1.62 tff(4579,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4140, 1, 1455, 340, 3986, 1055, 67, 66])).
% 1.44/1.62 tff(4580,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[325, 4579])).
% 1.44/1.62 tff(4581,plain,
% 1.44/1.62 (b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4580, 4578])).
% 1.44/1.62 tff(4582,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4053, 77, 360, 1027])).
% 1.44/1.62 tff(4583,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[870, 21, 829, 4582])).
% 1.44/1.62 tff(4584,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[916, 21, 913, 1028])).
% 1.44/1.62 tff(4585,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(elem!1)))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[556])).
% 1.44/1.62 tff(4586,plain,
% 1.44/1.62 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[557])).
% 1.44/1.62 tff(4587,plain,
% 1.44/1.62 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4586, 1393])).
% 1.44/1.62 tff(4588,plain,
% 1.44/1.62 ((~(s(s(elem!1)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4587])).
% 1.44/1.62 tff(4589,plain,
% 1.44/1.62 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[913, 4588])).
% 1.44/1.62 tff(4590,plain,
% 1.44/1.62 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[557])).
% 1.44/1.62 tff(4591,plain,
% 1.44/1.62 ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4590])).
% 1.44/1.62 tff(4592,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4593,plain,
% 1.44/1.62 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4594,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4593])).
% 1.44/1.62 tff(4595,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4594, 4592])).
% 1.44/1.62 tff(4596,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(4597,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4596, 4595])).
% 1.44/1.62 tff(4598,plain,
% 1.44/1.62 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4597, 77, 752, 1027])).
% 1.44/1.62 tff(4599,plain,
% 1.44/1.62 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4598, 4591])).
% 1.44/1.62 tff(4600,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)],[1405, 4599, 4589])).
% 1.44/1.62 tff(4601,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4600, 4585])).
% 1.44/1.62 tff(4602,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.44/1.62 tff(4603,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4604,plain,
% 1.44/1.62 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4605,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4604])).
% 1.44/1.62 tff(4606,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4605, 4603])).
% 1.44/1.62 tff(4607,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(4608,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4607, 4606])).
% 1.44/1.62 tff(4609,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4608, 116, 1436, 4602, 4601, 4584, 4583])).
% 1.44/1.62 tff(4610,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~(s(s(z)) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(4611,plain,
% 1.44/1.62 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4610, 4581, 4569, 4573, 4575, 4000])).
% 1.44/1.62 tff(4612,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[885, 4611, 4570])).
% 1.44/1.62 tff(4613,plain,
% 1.44/1.62 (s(elem!1) = s(s(s(z)))),
% 1.44/1.62 inference(symmetry,[status(thm)],[4576])).
% 1.44/1.62 tff(4614,plain,
% 1.44/1.62 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4613])).
% 1.44/1.62 tff(4615,plain,
% 1.44/1.62 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.44/1.62 inference(symmetry,[status(thm)],[4614])).
% 1.44/1.62 tff(4616,plain,
% 1.44/1.62 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4569])).
% 1.44/1.62 tff(4617,plain,
% 1.44/1.62 (b(s(s(s(z))), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[154, 4616])).
% 1.44/1.62 tff(4618,plain,
% 1.44/1.62 (b(s(elem!1), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4617, 4615])).
% 1.44/1.62 tff(4619,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4620,plain,
% 1.44/1.62 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4621,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4620])).
% 1.44/1.62 tff(4622,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4621, 4619])).
% 1.44/1.62 tff(4623,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(4624,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4623, 4622])).
% 1.44/1.62 tff(4625,plain,
% 1.44/1.62 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4624, 116, 3989, 667, 4618, 4612])).
% 1.44/1.62 tff(4626,plain,
% 1.44/1.62 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[836, 4569, 4572])).
% 1.44/1.62 tff(4627,plain,
% 1.44/1.62 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[858, 21, 4626, 4625])).
% 1.44/1.62 tff(4628,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4629,plain,
% 1.44/1.62 (((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4630,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4629])).
% 1.44/1.62 tff(4631,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4630, 4628])).
% 1.44/1.62 tff(4632,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(4633,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4632, 4631])).
% 1.44/1.62 tff(4634,plain,
% 1.44/1.62 (~b(s(s(s(s(s(z))))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4633, 116, 1055, 3989, 667, 4612])).
% 1.44/1.62 tff(4635,plain,
% 1.44/1.62 (r(s(s(s(s(s(z))))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[898, 21, 895, 4634])).
% 1.44/1.62 tff(4636,plain,
% 1.44/1.62 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4576])).
% 1.44/1.62 tff(4637,plain,
% 1.44/1.62 (r(s(elem!1), z)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[67, 4636])).
% 1.44/1.62 tff(4638,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4639,plain,
% 1.44/1.62 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), 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))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4640,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4639])).
% 1.44/1.62 tff(4641,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4640, 4638])).
% 1.44/1.62 tff(4642,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(4643,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4642, 4641])).
% 1.44/1.62 tff(4644,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4643, 77, 4637, 4635, 4627])).
% 1.44/1.62 tff(4645,plain,(b(s(s(z)), elem!1) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~r(s(s(s(z))), z)) | b(elem!1, z) | b(s(z), elem!1) | b(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(4646,plain,
% 1.44/1.62 (b(s(s(z)), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4645, 4568, 4565, 67, 1455, 340, 3986, 66])).
% 1.44/1.62 tff(4647,plain,
% 1.44/1.62 (~b(elem!1, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1340, 4646, 154, 152])).
% 1.44/1.62 tff(4648,plain,
% 1.44/1.62 (elem!1 = s(s(s(z)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1345, 4647, 4093])).
% 1.44/1.62 tff(4649,plain,
% 1.44/1.62 (s(elem!1) = s(s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4648])).
% 1.44/1.62 tff(4650,plain,
% 1.44/1.62 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4649])).
% 1.44/1.62 tff(4651,plain,
% 1.44/1.62 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4650])).
% 1.44/1.62 tff(4652,plain,
% 1.44/1.62 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4651])).
% 1.44/1.62 tff(4653,plain,
% 1.44/1.62 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4648])).
% 1.44/1.62 tff(4654,plain,
% 1.44/1.62 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4653])).
% 1.44/1.62 tff(4655,plain,
% 1.44/1.62 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3195, 4565, 3989, 4568])).
% 1.44/1.62 tff(4656,plain,
% 1.44/1.62 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4655, 4654])).
% 1.44/1.62 tff(4657,plain,
% 1.44/1.62 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4656, 4652])).
% 1.44/1.62 tff(4658,plain,
% 1.44/1.62 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1380, 4657])).
% 1.44/1.62 tff(4659,plain,
% 1.44/1.62 (~b(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3980, 4648, 340])).
% 1.44/1.62 tff(4660,plain,
% 1.44/1.62 (r(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[194, 4659])).
% 1.44/1.62 tff(4661,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2309, 77, 4660, 4658])).
% 1.44/1.62 tff(4662,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[870, 21, 1901, 4661])).
% 1.44/1.62 tff(4663,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4664,plain,
% 1.44/1.62 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4665,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4664])).
% 1.44/1.62 tff(4666,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4665, 4663])).
% 1.44/1.62 tff(4667,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(4668,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4667, 4666])).
% 1.44/1.62 tff(4669,plain,
% 1.44/1.62 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4668, 77, 3987, 4660])).
% 1.44/1.62 tff(4670,plain,
% 1.44/1.62 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2054, 21, 4669])).
% 1.44/1.62 tff(4671,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4670, 2044])).
% 1.44/1.62 tff(4672,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(4673,assumption,(~(s(s(s(s(s(z))))) = s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(4674,plain,
% 1.44/1.62 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1379, 4673, 4672])).
% 1.44/1.62 tff(4675,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4676,plain,
% 1.44/1.62 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(4677,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4676])).
% 1.44/1.62 tff(4678,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4677, 4675])).
% 1.44/1.62 tff(4679,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(4680,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[4679, 4678])).
% 1.44/1.62 tff(4681,plain,
% 1.44/1.62 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4680, 77, 3953, 4674])).
% 1.44/1.62 tff(4682,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.62 tff(4683,plain,
% 1.44/1.62 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1940, 21, 4682])).
% 1.44/1.62 tff(4684,plain,
% 1.44/1.62 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4683, 4681])).
% 1.44/1.62 tff(4685,plain,
% 1.44/1.62 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4684])).
% 1.44/1.62 tff(4686,plain,
% 1.44/1.62 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[4685])).
% 1.44/1.62 tff(4687,plain,
% 1.44/1.62 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[4684])).
% 1.44/1.62 tff(4688,plain,
% 1.44/1.62 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4687, 554, 4686, 127])).
% 1.44/1.62 tff(4689,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4673, 4688])).
% 1.44/1.62 tff(4690,plain,((s(s(s(s(s(z))))) = 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(z))))) | b(s(s(s(s(s(z))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(4691,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4690, 1138])).
% 1.44/1.62 tff(4692,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[4691, 4657, 3987])).
% 1.44/1.62 tff(4693,plain,
% 1.44/1.62 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4649])).
% 1.44/1.62 tff(4694,plain,
% 1.44/1.62 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[4693, 1393])).
% 1.44/1.62 tff(4695,plain,
% 1.44/1.62 ((~(s(elem!1) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[4694])).
% 1.44/1.62 tff(4696,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3975, 4660, 3987])).
% 1.44/1.62 tff(4697,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[325, 4696])).
% 1.44/1.62 tff(4698,plain,
% 1.44/1.62 (b(s(z), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[249, 3869])).
% 1.44/1.62 tff(4699,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[340, 4698])).
% 1.44/1.62 tff(4700,plain,((~(elem!1 = s(s(s(s(z)))))) | b(s(z), elem!1) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4701,plain,
% 1.44/1.63 (~(elem!1 = s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4700, 4697, 340])).
% 1.44/1.63 tff(4702,plain,
% 1.44/1.63 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1364, 4701])).
% 1.44/1.63 tff(4703,plain,
% 1.44/1.63 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4702, 4695])).
% 1.44/1.63 tff(4704,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4705,plain,
% 1.44/1.63 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4706,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4705])).
% 1.44/1.63 tff(4707,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[4706, 4704])).
% 1.44/1.63 tff(4708,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(4709,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(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))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4708, 4707])).
% 1.44/1.63 tff(4710,plain,
% 1.44/1.63 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4709, 77, 3987, 4658])).
% 1.44/1.63 tff(4711,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1405, 4710, 4703])).
% 1.44/1.63 tff(4712,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4713,plain,
% 1.44/1.63 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4714,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4713])).
% 1.44/1.63 tff(4715,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[4714, 4712])).
% 1.44/1.63 tff(4716,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(4717,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4716, 4715])).
% 1.44/1.63 tff(4718,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4717, 116, 4711, 4692, 4671, 4662])).
% 1.44/1.63 tff(4719,plain,(b(elem!1, z) | b(s(z), elem!1) | (~r(s(s(s(z))), z)) | b(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4720,plain,
% 1.44/1.63 (b(elem!1, z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4719, 64, 340, 3946, 26, 4562])).
% 1.44/1.63 tff(4721,plain,
% 1.44/1.63 (~(elem!1 = s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1470, 4720, 57])).
% 1.44/1.63 tff(4722,plain,
% 1.44/1.63 (~(s(s(z)) = elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[540, 4720, 2])).
% 1.44/1.63 tff(4723,plain,
% 1.44/1.63 (~r(s(s(s(s(z)))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3961, 67, 3953])).
% 1.44/1.63 tff(4724,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[247, 4723])).
% 1.44/1.63 tff(4725,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4726,plain,
% 1.44/1.63 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4727,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4726])).
% 1.44/1.63 tff(4728,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[4727, 4725])).
% 1.44/1.63 tff(4729,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(4730,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4729, 4728])).
% 1.44/1.63 tff(4731,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4730, 116, 1055, 537, 270, 254, 249])).
% 1.44/1.63 tff(4732,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4733,plain,
% 1.44/1.63 (~b(s(z), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4732, 4210, 3989, 537, 4724])).
% 1.44/1.63 tff(4734,plain,
% 1.44/1.63 (r(s(z), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[325, 4733])).
% 1.44/1.63 tff(4735,plain,
% 1.44/1.63 (~r(s(z), s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4391, 428, 4724, 537, 66, 67, 340])).
% 1.44/1.63 tff(4736,plain,
% 1.44/1.63 (b(s(z), s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[172, 4735])).
% 1.44/1.63 tff(4737,plain,
% 1.44/1.63 (~b(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[184, 4736, 154, 152])).
% 1.44/1.63 tff(4738,plain,
% 1.44/1.63 (r(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[194, 4737])).
% 1.44/1.63 tff(4739,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3975, 4738, 4734, 3953])).
% 1.44/1.63 tff(4740,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4741,plain,
% 1.44/1.63 (~r(s(s(z)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4740, 4720, 3952, 26, 64, 340])).
% 1.44/1.63 tff(4742,plain,
% 1.44/1.63 (b(s(s(z)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[426, 4741, 4722])).
% 1.44/1.63 tff(4743,plain,
% 1.44/1.63 (~b(elem!1, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1340, 4742, 90, 106])).
% 1.44/1.63 tff(4744,plain,
% 1.44/1.63 (r(elem!1, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1345, 4743, 4721])).
% 1.44/1.63 tff(4745,plain,
% 1.44/1.63 (~(elem!1 = z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[409, 211, 340])).
% 1.44/1.63 tff(4746,plain,
% 1.44/1.63 (~(z = elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[445, 4745])).
% 1.44/1.63 tff(4747,plain,
% 1.44/1.63 (~r(s(z), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3295, 448, 293])).
% 1.44/1.63 tff(4748,plain,
% 1.44/1.63 (s(z) = elem!1),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[357, 4747, 340])).
% 1.44/1.63 tff(4749,plain,
% 1.44/1.63 (s(s(z)) = s(elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4748])).
% 1.44/1.63 tff(4750,plain,
% 1.44/1.63 (s(s(s(z))) = s(s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4749])).
% 1.44/1.63 tff(4751,plain,
% 1.44/1.63 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[4750])).
% 1.44/1.63 tff(4752,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4751])).
% 1.44/1.63 tff(4753,plain,
% 1.44/1.63 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.63 inference(symmetry,[status(thm)],[4752])).
% 1.44/1.63 tff(4754,plain,
% 1.44/1.63 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4749])).
% 1.44/1.63 tff(4755,plain,
% 1.44/1.63 (b(s(s(s(z))), s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[176, 4754])).
% 1.44/1.63 tff(4756,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4755, 4753])).
% 1.44/1.63 tff(4757,plain,
% 1.44/1.63 (b(s(elem!1), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1549, 4748, 1331])).
% 1.44/1.63 tff(4758,plain,
% 1.44/1.63 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4750])).
% 1.44/1.63 tff(4759,plain,
% 1.44/1.63 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4758])).
% 1.44/1.63 tff(4760,plain,
% 1.44/1.63 (~(elem!1 = s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1470, 1975, 57])).
% 1.44/1.63 tff(4761,plain,
% 1.44/1.63 (r(elem!1, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1345, 4760, 1355])).
% 1.44/1.63 tff(4762,plain,
% 1.44/1.63 (r(elem!1, s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4761, 1619])).
% 1.44/1.63 tff(4763,plain,
% 1.44/1.63 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1475])).
% 1.44/1.63 tff(4764,plain,
% 1.44/1.63 (r(z, s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[291, 4763])).
% 1.44/1.63 tff(4765,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[500, 77, 448, 4764, 4762])).
% 1.44/1.63 tff(4766,plain,((~(s(z) = elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4767,plain,
% 1.44/1.63 (~r(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4766, 4748, 57, 1355, 448, 270])).
% 1.44/1.63 tff(4768,plain,
% 1.44/1.63 (~r(z, s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4767, 4759])).
% 1.44/1.63 tff(4769,plain,
% 1.44/1.63 (b(z, s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[514, 4768])).
% 1.44/1.63 tff(4770,plain,
% 1.44/1.63 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4748])).
% 1.44/1.63 tff(4771,plain,
% 1.44/1.63 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4770])).
% 1.44/1.63 tff(4772,plain,
% 1.44/1.63 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[566, 4771])).
% 1.44/1.63 tff(4773,plain,
% 1.44/1.63 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4750])).
% 1.44/1.63 tff(4774,plain,
% 1.44/1.63 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4773])).
% 1.44/1.63 tff(4775,plain,
% 1.44/1.63 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4748])).
% 1.44/1.63 tff(4776,plain,
% 1.44/1.63 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(z))), elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4775])).
% 1.44/1.63 tff(4777,plain,
% 1.44/1.63 (~r(s(s(s(z))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1489, 4748, 64, 448])).
% 1.44/1.63 tff(4778,plain,
% 1.44/1.63 (~r(s(s(s(z))), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4777, 4776])).
% 1.44/1.63 tff(4779,plain,
% 1.44/1.63 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4778, 4774])).
% 1.44/1.63 tff(4780,plain,
% 1.44/1.63 (b(s(s(elem!1)), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[743, 4779, 4772])).
% 1.44/1.63 tff(4781,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4782,plain,
% 1.44/1.63 (((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4783,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4782])).
% 1.44/1.63 tff(4784,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[4783, 4781])).
% 1.44/1.63 tff(4785,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(4786,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4785, 4784])).
% 1.44/1.63 tff(4787,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4786, 116, 537, 4780, 4769, 4757, 4756])).
% 1.44/1.63 tff(4788,plain,((~r(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(s(z))), z) | b(elem!1, s(s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), elem!1)) | b(s(z), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4789,plain,
% 1.44/1.63 (~r(z, elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4788, 4720, 90, 57, 4743, 211, 4742, 340, 4562])).
% 1.44/1.63 tff(4790,plain,
% 1.44/1.63 (b(z, elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1044, 4789, 4746])).
% 1.44/1.63 tff(4791,plain,
% 1.44/1.63 (b(z, s(z)) <=> b(z, elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[466])).
% 1.44/1.63 tff(4792,plain,
% 1.44/1.63 (b(z, elem!1) <=> b(z, s(z))),
% 1.44/1.63 inference(symmetry,[status(thm)],[4791])).
% 1.44/1.63 tff(4793,plain,
% 1.44/1.63 (b(z, s(z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1055, 4792])).
% 1.44/1.63 tff(4794,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.44/1.63 tff(4795,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4794, 4793])).
% 1.44/1.63 tff(4796,plain,((~(s(z) = elem!1)) | b(z, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4797,plain,
% 1.44/1.63 (~(s(z) = elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4796, 4790, 4561])).
% 1.44/1.63 tff(4798,plain,
% 1.44/1.63 (r(s(z), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[357, 4797, 340])).
% 1.44/1.63 tff(4799,plain,
% 1.44/1.63 (~r(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[368, 4798, 4744])).
% 1.44/1.63 tff(4800,plain,
% 1.44/1.63 (b(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[194, 4799])).
% 1.44/1.63 tff(4801,plain,
% 1.44/1.63 (~b(s(s(z)), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4427, 116, 106, 90, 4800])).
% 1.44/1.63 tff(4802,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[391, 21, 4801, 388, 4563])).
% 1.44/1.63 tff(4803,plain,(b(s(s(s(z))), z) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(4804,plain,
% 1.44/1.63 (b(s(s(s(z))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4803, 340, 2])).
% 1.44/1.63 tff(4805,plain,
% 1.44/1.63 (~(elem!1 = s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2407, 1455, 4804])).
% 1.44/1.63 tff(4806,plain,
% 1.44/1.63 (r(s(elem!1), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[360, 1761])).
% 1.44/1.63 tff(4807,plain,
% 1.44/1.63 (~r(s(s(elem!1)), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[758, 77, 1825, 4806])).
% 1.44/1.63 tff(4808,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[767, 4807, 1791])).
% 1.44/1.63 tff(4809,plain,
% 1.44/1.63 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1709, 1784])).
% 1.44/1.63 tff(4810,plain,
% 1.44/1.63 (~r(s(z), s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4008, 1714, 360])).
% 1.44/1.63 tff(4811,plain,
% 1.44/1.63 (b(s(z), s(s(z)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[172, 4810])).
% 1.44/1.63 tff(4812,plain,
% 1.44/1.63 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4811, 4809])).
% 1.44/1.63 tff(4813,plain,
% 1.44/1.63 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[855, 4213])).
% 1.44/1.63 tff(4814,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4815,plain,
% 1.44/1.63 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4816,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4815])).
% 1.44/1.63 tff(4817,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[4816, 4814])).
% 1.44/1.63 tff(4818,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(4819,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4818, 4817])).
% 1.44/1.63 tff(4820,plain,
% 1.44/1.63 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4819, 77, 1027, 650])).
% 1.44/1.63 tff(4821,plain,
% 1.44/1.63 ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4324, 21, 4820])).
% 1.44/1.63 tff(4822,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4821, 4813])).
% 1.44/1.63 tff(4823,plain,
% 1.44/1.63 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1504])).
% 1.44/1.63 tff(4824,plain,
% 1.44/1.63 ((~(s(s(elem!1)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[4823])).
% 1.44/1.63 tff(4825,plain,
% 1.44/1.63 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[953, 4824])).
% 1.44/1.63 tff(4826,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(4827,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(4828,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[4827, 4826])).
% 1.44/1.63 tff(4829,plain,
% 1.44/1.63 ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4828, 21, 4598])).
% 1.44/1.63 tff(4830,plain,
% 1.44/1.63 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[4829, 4825])).
% 1.44/1.63 tff(4831,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4832,plain,
% 1.44/1.64 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4833,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4832])).
% 1.44/1.64 tff(4834,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[4833, 4831])).
% 1.44/1.64 tff(4835,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(4836,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4835, 4834])).
% 1.44/1.64 tff(4837,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4836, 116, 1878, 1877, 4830, 4822])).
% 1.44/1.64 tff(4838,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(4839,plain,
% 1.44/1.64 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4838, 4812, 4808, 1902, 1955, 4806, 1825])).
% 1.44/1.64 tff(4840,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[885, 4839, 1896])).
% 1.44/1.64 tff(4841,plain,
% 1.44/1.64 (~b(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[409, 1713, 340])).
% 1.44/1.64 tff(4842,plain,
% 1.44/1.64 (r(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[210, 4841])).
% 1.44/1.64 tff(4843,plain,
% 1.44/1.64 (~r(s(s(s(s(z)))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2285, 4842, 26])).
% 1.44/1.64 tff(4844,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[247, 4843])).
% 1.44/1.64 tff(4845,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4844, 1719])).
% 1.44/1.64 tff(4846,plain,
% 1.44/1.64 (b(s(s(s(z))), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4804, 3547])).
% 1.44/1.64 tff(4847,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4848,plain,
% 1.44/1.64 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4849,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4848])).
% 1.44/1.64 tff(4850,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[4849, 4847])).
% 1.44/1.64 tff(4851,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(4852,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4851, 4850])).
% 1.44/1.64 tff(4853,plain,
% 1.44/1.64 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4852, 116, 3561, 1332, 845])).
% 1.44/1.64 tff(4854,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4855,plain,
% 1.44/1.64 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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)))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4856,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4855])).
% 1.44/1.64 tff(4857,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[4856, 4854])).
% 1.44/1.64 tff(4858,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(4859,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4858, 4857])).
% 1.44/1.64 tff(4860,plain,
% 1.44/1.64 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4859, 116, 3561, 1332, 1725, 845])).
% 1.44/1.64 tff(4861,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4691, 4860, 4853, 3953])).
% 1.44/1.64 tff(4862,plain,((~b(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(4863,plain,
% 1.44/1.64 (~b(elem!1, s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4862, 4846, 3952, 4845, 4840])).
% 1.44/1.64 tff(4864,plain,
% 1.44/1.64 (r(elem!1, s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1345, 4863, 1620])).
% 1.44/1.64 tff(4865,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[404])).
% 1.44/1.64 tff(4866,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[845, 4865])).
% 1.44/1.64 tff(4867,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.44/1.64 tff(4868,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4867, 4866])).
% 1.44/1.64 tff(4869,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(z))))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(4870,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4869, 4840, 1713])).
% 1.44/1.64 tff(4871,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4872,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(4873,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4872, 4871])).
% 1.44/1.64 tff(4874,plain,
% 1.44/1.64 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4873, 116, 2247, 254, 954, 1176])).
% 1.44/1.64 tff(4875,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4876,plain,
% 1.44/1.64 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4877,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4876])).
% 1.44/1.64 tff(4878,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[4877, 4875])).
% 1.44/1.64 tff(4879,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(4880,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4879, 4878])).
% 1.44/1.64 tff(4881,plain,
% 1.44/1.64 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4880, 116, 254, 954, 1176])).
% 1.44/1.64 tff(4882,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4691, 4881, 4874, 3953])).
% 1.44/1.64 tff(4883,plain,((~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(4884,plain,
% 1.44/1.64 (~b(z, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4883, 4870, 4804, 4844, 3952])).
% 1.44/1.64 tff(4885,plain,
% 1.44/1.64 (~b(elem!1, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3626, 4884, 442])).
% 1.44/1.64 tff(4886,plain,
% 1.44/1.64 (r(elem!1, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1068, 4885, 1718])).
% 1.44/1.64 tff(4887,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4401, 77, 4886, 3952, 4864])).
% 1.44/1.64 tff(4888,plain,((~(z = elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(z), elem!1)) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(4889,plain,
% 1.44/1.64 (~(z = elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4888, 360, 4805, 340, 2])).
% 1.44/1.64 tff(4890,plain,
% 1.44/1.64 (~(elem!1 = z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[533, 4889])).
% 1.44/1.64 tff(4891,plain,
% 1.44/1.64 (r(elem!1, z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[545, 4890, 1455])).
% 1.44/1.64 tff(4892,plain,
% 1.44/1.64 (~r(s(s(z)), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1319, 77, 4891, 26])).
% 1.44/1.64 tff(4893,plain,
% 1.44/1.64 (s(s(z)) = elem!1),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[426, 4892, 1])).
% 1.44/1.64 tff(4894,plain,
% 1.44/1.64 (s(s(s(z))) = s(elem!1)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4893])).
% 1.44/1.64 tff(4895,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4894])).
% 1.44/1.64 tff(4896,plain,
% 1.44/1.64 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4894])).
% 1.44/1.64 tff(4897,plain,
% 1.44/1.64 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[4896])).
% 1.44/1.64 tff(4898,plain,
% 1.44/1.64 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4897])).
% 1.44/1.64 tff(4899,plain,
% 1.44/1.64 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4898])).
% 1.44/1.64 tff(4900,plain,
% 1.44/1.64 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[568, 4893])).
% 1.44/1.64 tff(4901,plain,
% 1.44/1.64 (~(s(elem!1) = s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[842, 4893])).
% 1.44/1.64 tff(4902,plain,
% 1.44/1.64 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[529, 4893, 4889])).
% 1.44/1.64 tff(4903,plain,
% 1.44/1.64 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[836, 4893, 4902])).
% 1.44/1.64 tff(4904,plain,
% 1.44/1.64 (~r(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2815, 4891, 360])).
% 1.44/1.64 tff(4905,plain,
% 1.44/1.64 (b(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[210, 4904])).
% 1.44/1.64 tff(4906,plain,
% 1.44/1.64 (~b(s(z), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[376, 4893, 340])).
% 1.44/1.64 tff(4907,plain,
% 1.44/1.64 (r(s(z), s(s(z)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[172, 4906])).
% 1.44/1.64 tff(4908,plain,
% 1.44/1.64 (~b(z, elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3243, 4907, 26, 4804, 4893, 360, 4805])).
% 1.44/1.64 tff(4909,plain,
% 1.44/1.64 (r(z, elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1044, 4908, 4889])).
% 1.44/1.64 tff(4910,plain,
% 1.44/1.64 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4894])).
% 1.44/1.64 tff(4911,plain,
% 1.44/1.64 (b(s(elem!1), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4804, 4910])).
% 1.44/1.64 tff(4912,plain,
% 1.44/1.64 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3807, 4911, 1901, 4909, 4905, 4903, 4901])).
% 1.44/1.64 tff(4913,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[885, 4912, 4900])).
% 1.44/1.64 tff(4914,plain,
% 1.44/1.64 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4897])).
% 1.44/1.64 tff(4915,plain,
% 1.44/1.64 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.44/1.64 inference(symmetry,[status(thm)],[4914])).
% 1.44/1.64 tff(4916,plain,
% 1.44/1.64 (~r(z, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3295, 4909, 360])).
% 1.44/1.64 tff(4917,plain,
% 1.44/1.64 (b(z, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[289, 4916])).
% 1.44/1.64 tff(4918,plain,
% 1.44/1.64 (~b(s(z), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3291, 4917, 4804, 4905])).
% 1.44/1.64 tff(4919,plain,
% 1.44/1.64 (r(s(z), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[194, 4918])).
% 1.44/1.64 tff(4920,plain,
% 1.44/1.64 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3975, 4919, 3952])).
% 1.44/1.64 tff(4921,plain,
% 1.44/1.64 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[325, 4920])).
% 1.44/1.64 tff(4922,plain,
% 1.44/1.64 (~(elem!1 = s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4700, 4921, 340])).
% 1.44/1.64 tff(4923,plain,
% 1.44/1.64 (~b(s(s(s(s(z)))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[279, 4921, 4905, 4917])).
% 1.44/1.64 tff(4924,plain,
% 1.44/1.64 (r(s(s(s(s(z)))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[247, 4923])).
% 1.44/1.64 tff(4925,plain,
% 1.44/1.64 (~r(elem!1, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2671, 4924, 4891])).
% 1.44/1.64 tff(4926,plain,
% 1.44/1.64 (b(elem!1, s(s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1068, 4925, 4922])).
% 1.44/1.64 tff(4927,plain,
% 1.44/1.64 (b(elem!1, s(s(elem!1)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4926, 4915])).
% 1.44/1.64 tff(4928,plain,
% 1.44/1.64 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1446, 4909, 4905, 360])).
% 1.44/1.64 tff(4929,plain,
% 1.44/1.64 (b(s(s(elem!1)), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[743, 4928, 4902])).
% 1.44/1.64 tff(4930,plain,
% 1.44/1.64 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3820, 116, 4929, 4927, 4913])).
% 1.44/1.64 tff(4931,plain,
% 1.44/1.64 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4930, 4899])).
% 1.44/1.64 tff(4932,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4691, 4931, 3952])).
% 1.44/1.64 tff(4933,plain,
% 1.44/1.64 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4932, 4895])).
% 1.44/1.64 tff(4934,plain,
% 1.44/1.64 (s(elem!1) = s(s(s(z)))),
% 1.44/1.64 inference(symmetry,[status(thm)],[4894])).
% 1.44/1.64 tff(4935,plain,
% 1.44/1.64 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4934])).
% 1.44/1.64 tff(4936,plain,
% 1.44/1.64 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.44/1.64 inference(symmetry,[status(thm)],[4935])).
% 1.44/1.64 tff(4937,plain,
% 1.44/1.64 (~r(elem!1, s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3062, 4909, 4804, 360, 4891])).
% 1.44/1.64 tff(4938,plain,
% 1.44/1.64 (b(elem!1, s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1345, 4937, 4805])).
% 1.44/1.64 tff(4939,plain,
% 1.44/1.64 (b(elem!1, s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4938, 4936])).
% 1.44/1.64 tff(4940,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4941,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(4942,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4941, 4940])).
% 1.44/1.64 tff(4943,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4942, 116, 4917, 4911, 4939, 4913, 4933])).
% 1.44/1.64 tff(4944,plain,((~r(s(z), elem!1)) | b(s(z), elem!1) | b(s(s(z)), elem!1) | b(elem!1, z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(4945,plain,
% 1.44/1.64 (~r(s(z), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4944, 1, 340, 1455, 2])).
% 1.44/1.64 tff(4946,plain,
% 1.44/1.64 (s(z) = elem!1),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[357, 4945, 340])).
% 1.44/1.64 tff(4947,plain,
% 1.44/1.64 (s(s(z)) = s(elem!1)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4946])).
% 1.44/1.64 tff(4948,plain,
% 1.44/1.64 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4947])).
% 1.44/1.64 tff(4949,plain,
% 1.44/1.64 (~(s(s(z)) = elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[480, 4946])).
% 1.44/1.64 tff(4950,plain,
% 1.44/1.64 (r(s(s(z)), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[426, 4949, 1])).
% 1.44/1.64 tff(4951,plain,
% 1.44/1.64 (r(s(elem!1), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4950, 4948])).
% 1.44/1.64 tff(4952,plain,
% 1.44/1.64 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4947])).
% 1.44/1.64 tff(4953,plain,
% 1.44/1.64 (r(s(elem!1), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[26, 4952])).
% 1.44/1.64 tff(4954,plain,
% 1.44/1.64 (r(s(z), z) <=> r(elem!1, z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4946])).
% 1.44/1.64 tff(4955,plain,
% 1.44/1.64 (~b(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1458, 4946, 1455])).
% 1.44/1.64 tff(4956,plain,
% 1.44/1.64 (r(s(z), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[210, 4955])).
% 1.44/1.64 tff(4957,plain,
% 1.44/1.64 (r(elem!1, z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4956, 4954])).
% 1.44/1.64 tff(4958,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4959,plain,
% 1.44/1.64 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(4960,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[4959])).
% 1.44/1.64 tff(4961,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[4960, 4958])).
% 1.44/1.64 tff(4962,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(4963,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[4962, 4961])).
% 1.44/1.64 tff(4964,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4963, 77, 4957, 4953, 4951])).
% 1.44/1.64 tff(4965,plain,(b(s(s(z)), elem!1) | b(elem!1, z) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(4966,plain,
% 1.44/1.64 (b(s(s(z)), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[4965, 1455, 340, 2])).
% 1.44/1.64 tff(4967,plain,
% 1.44/1.64 (~(s(s(z)) = elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[376, 173, 340])).
% 1.44/1.64 tff(4968,plain,
% 1.44/1.64 (r(s(s(z)), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[426, 4967, 1])).
% 1.44/1.64 tff(4969,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(4970,plain,
% 1.44/1.65 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(4971,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[4970])).
% 1.44/1.65 tff(4972,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[4971, 4969])).
% 1.44/1.65 tff(4973,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(4974,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[4973, 4972])).
% 1.44/1.65 tff(4975,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4974, 77, 2235, 428, 638])).
% 1.44/1.65 tff(4976,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(4977,plain,
% 1.44/1.65 (~r(s(s(s(z))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4976, 4968, 2235])).
% 1.44/1.65 tff(4978,plain,
% 1.44/1.65 (b(s(s(z)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[391, 21, 388, 2264])).
% 1.44/1.65 tff(4979,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(4980,plain,
% 1.44/1.65 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(4981,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[4980])).
% 1.44/1.65 tff(4982,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[4981, 4979])).
% 1.44/1.65 tff(4983,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(4984,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[4983, 4982])).
% 1.44/1.65 tff(4985,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4984, 77, 2235, 3953])).
% 1.44/1.65 tff(4986,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[226, 4985])).
% 1.44/1.65 tff(4987,plain,
% 1.44/1.65 (~b(s(z), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2272, 116, 4986, 4978, 173])).
% 1.44/1.65 tff(4988,plain,
% 1.44/1.65 (r(s(z), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[325, 4987])).
% 1.44/1.65 tff(4989,plain,
% 1.44/1.65 (~r(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3975, 4988, 3953])).
% 1.44/1.65 tff(4990,plain,
% 1.44/1.65 (b(s(z), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[194, 4989])).
% 1.44/1.65 tff(4991,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1380, 4672])).
% 1.44/1.65 tff(4992,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(4993,plain,
% 1.44/1.65 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(4994,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[4993])).
% 1.44/1.65 tff(4995,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[4994, 4992])).
% 1.44/1.65 tff(4996,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(4997,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(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(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[4996, 4995])).
% 1.44/1.65 tff(4998,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[4997, 77, 2235, 4991])).
% 1.44/1.65 tff(4999,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 4998])).
% 1.44/1.65 tff(5000,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)],[4691, 4672, 3953])).
% 1.44/1.65 tff(5001,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5002,plain,
% 1.44/1.65 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5003,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5002])).
% 1.44/1.65 tff(5004,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5003, 5001])).
% 1.44/1.65 tff(5005,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5006,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5005, 5004])).
% 1.44/1.65 tff(5007,plain,
% 1.44/1.65 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5006, 77, 2235, 3953])).
% 1.44/1.65 tff(5008,plain,
% 1.44/1.65 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[149, 5007])).
% 1.44/1.65 tff(5009,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5010,plain,
% 1.44/1.65 (((~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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5011,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5010])).
% 1.44/1.65 tff(5012,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5011, 5009])).
% 1.44/1.65 tff(5013,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5014,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5013, 5012])).
% 1.44/1.65 tff(5015,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5014, 116, 4986, 5008, 5000, 4999])).
% 1.44/1.65 tff(5016,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5017,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5016, 2235, 3953])).
% 1.44/1.65 tff(5018,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5019,plain,
% 1.44/1.65 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5020,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5019])).
% 1.44/1.65 tff(5021,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5020, 5018])).
% 1.44/1.65 tff(5022,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5023,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5022, 5021])).
% 1.44/1.65 tff(5024,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5023, 77, 2235, 428, 359])).
% 1.44/1.65 tff(5025,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5026,plain,
% 1.44/1.65 (~r(elem!1, s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5025, 4968, 2235])).
% 1.44/1.65 tff(5027,plain,
% 1.44/1.65 (b(elem!1, s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1345, 5026, 3467])).
% 1.44/1.65 tff(5028,plain,
% 1.44/1.65 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[442])).
% 1.44/1.65 tff(5029,plain,
% 1.44/1.65 (r(s(z), elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[155, 5028])).
% 1.44/1.65 tff(5030,plain,
% 1.44/1.65 (r(s(elem!1), elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5029, 1761])).
% 1.44/1.65 tff(5031,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.44/1.65 tff(5032,plain,
% 1.44/1.65 (b(s(s(s(z))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2725, 1750, 2719])).
% 1.44/1.65 tff(5033,plain,
% 1.44/1.65 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~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))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5034,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5033])).
% 1.44/1.65 tff(5035,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5034, 4847])).
% 1.44/1.65 tff(5036,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5037,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 1.44/1.65 tff(5038,plain,
% 1.44/1.65 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5037, 116, 5032, 1332, 5031])).
% 1.44/1.65 tff(5039,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[885, 5038, 1896])).
% 1.44/1.65 tff(5040,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5041,plain,
% 1.44/1.65 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5042,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5041])).
% 1.44/1.65 tff(5043,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5042, 5040])).
% 1.44/1.65 tff(5044,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5045,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 1.44/1.65 tff(5046,plain,
% 1.44/1.65 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5045, 77, 5039, 5030])).
% 1.44/1.65 tff(5047,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[1710])).
% 1.44/1.65 tff(5048,plain,
% 1.44/1.65 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[5047])).
% 1.44/1.65 tff(5049,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[175, 5048])).
% 1.44/1.65 tff(5050,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), 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))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5051,plain,
% 1.44/1.65 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), 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))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(5052,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), 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)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5051])).
% 1.44/1.65 tff(5053,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), 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))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[5052, 5050])).
% 1.44/1.65 tff(5054,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(5055,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5054, 5053])).
% 1.44/1.65 tff(5056,plain,
% 1.44/1.65 ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5055, 116, 5032, 1332, 5031])).
% 1.44/1.65 tff(5057,plain,
% 1.44/1.65 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5056, 5049])).
% 1.44/1.65 tff(5058,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[858, 21, 1902, 5057, 5046])).
% 1.44/1.65 tff(5059,plain,((~(z = elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5060,plain,
% 1.44/1.65 (~(z = elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5059, 5027, 5017, 4990, 155, 4977])).
% 1.44/1.65 tff(5061,plain,
% 1.44/1.65 (~(elem!1 = z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[533, 5060])).
% 1.44/1.65 tff(5062,plain,
% 1.44/1.65 (r(elem!1, z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[545, 5061, 1455])).
% 1.44/1.65 tff(5063,plain,
% 1.44/1.65 (~r(s(z), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2815, 5062, 155])).
% 1.44/1.65 tff(5064,plain,
% 1.44/1.65 (s(z) = elem!1),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[357, 5063, 340])).
% 1.44/1.65 tff(5065,plain,
% 1.44/1.65 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[5064])).
% 1.44/1.65 tff(5066,plain,
% 1.44/1.65 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(z))),
% 1.44/1.65 inference(symmetry,[status(thm)],[5065])).
% 1.44/1.65 tff(5067,plain,
% 1.44/1.65 (b(z, elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1044, 5060, 1052])).
% 1.44/1.65 tff(5068,plain,
% 1.44/1.65 (~b(s(s(s(z))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2767, 5067, 2247, 5027])).
% 1.44/1.65 tff(5069,plain,
% 1.44/1.65 (s(s(s(z))) = elem!1),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2725, 5068, 4977])).
% 1.44/1.65 tff(5070,plain,
% 1.44/1.65 (s(s(s(z))) = s(z)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[5069, 5066])).
% 1.44/1.65 tff(5071,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[135, 5070])).
% 1.44/1.65 tff(5072,plain,((~r(s(z), z)) | b(s(z), elem!1) | (~b(s(s(s(z))), z)) | b(elem!1, z) | r(z, elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(5073,plain,
% 1.44/1.65 (~r(s(z), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[5072, 1052, 2247, 1455, 340, 3953, 66, 2235, 1])).
% 1.44/1.65 tff(5074,plain,
% 1.44/1.65 (b(s(z), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[210, 5073])).
% 1.44/1.65 tff(5075,plain,
% 1.44/1.65 (~(elem!1 = z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[409, 5074, 340])).
% 1.44/1.65 tff(5076,plain,
% 1.44/1.65 (r(elem!1, z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[545, 5075, 1455])).
% 1.44/1.65 tff(5077,plain,
% 1.44/1.65 (~r(s(s(z)), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1319, 77, 5076, 66])).
% 1.44/1.65 tff(5078,plain,
% 1.44/1.65 (s(s(z)) = elem!1),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[426, 5077, 1])).
% 1.44/1.65 tff(5079,plain,
% 1.44/1.65 (~b(s(z), s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[376, 5078, 340])).
% 1.44/1.65 tff(5080,plain,
% 1.44/1.65 (~(s(z) = elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1458, 5074, 1455])).
% 1.44/1.65 tff(5081,plain,
% 1.44/1.65 (r(s(z), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[357, 5080, 340])).
% 1.44/1.65 tff(5082,plain,
% 1.44/1.65 (~(z = elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[445, 5075])).
% 1.44/1.65 tff(5083,plain,
% 1.44/1.65 (b(z, elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1044, 5082, 1052])).
% 1.44/1.66 tff(5084,plain,
% 1.44/1.66 (~r(s(z), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3243, 5078, 66, 2247, 5083, 5081, 3467])).
% 1.44/1.66 tff(5085,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[172, 5084, 5079])).
% 1.44/1.66 tff(5086,plain,(r(z, elem!1) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | b(s(z), elem!1) | b(s(s(z)), elem!1) | b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5087,plain,
% 1.44/1.66 (r(z, elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5086, 1, 2247, 340, 66, 1455, 3953, 2235])).
% 1.44/1.66 tff(5088,plain,
% 1.44/1.66 (~r(s(s(z)), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[456, 5087, 66])).
% 1.44/1.66 tff(5089,plain,
% 1.44/1.66 (s(s(z)) = elem!1),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[426, 5088, 1])).
% 1.44/1.66 tff(5090,plain,
% 1.44/1.66 (~(s(z) = elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[480, 5089])).
% 1.44/1.66 tff(5091,plain,
% 1.44/1.66 (r(s(z), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[357, 5090, 340])).
% 1.44/1.66 tff(5092,plain,
% 1.44/1.66 (~r(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[690, 5091, 5087])).
% 1.44/1.66 tff(5093,plain,
% 1.44/1.66 (b(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[210, 5092])).
% 1.44/1.66 tff(5094,plain,
% 1.44/1.66 (~r(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3295, 5091, 5087])).
% 1.44/1.66 tff(5095,plain,
% 1.44/1.66 (b(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[289, 5094])).
% 1.44/1.66 tff(5096,plain,
% 1.44/1.66 (~b(s(z), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[376, 5089, 340])).
% 1.44/1.66 tff(5097,plain,
% 1.44/1.66 (r(s(z), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[172, 5096])).
% 1.44/1.66 tff(5098,plain,
% 1.44/1.66 (~r(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2319, 5097, 2235])).
% 1.44/1.66 tff(5099,plain,
% 1.44/1.66 (b(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[194, 5098])).
% 1.44/1.66 tff(5100,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3291, 5099, 5095, 2247, 5093])).
% 1.44/1.66 tff(5101,plain,(b(s(s(z)), elem!1) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | b(s(z), elem!1) | (~r(s(s(z)), z)) | b(elem!1, z) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5102,plain,
% 1.44/1.66 (b(s(s(z)), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5101, 2235, 4804, 340, 26, 1455, 3952])).
% 1.44/1.66 tff(5103,plain,
% 1.44/1.66 (~(elem!1 = z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1680, 5102, 2])).
% 1.44/1.66 tff(5104,plain,
% 1.44/1.66 (r(elem!1, z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[545, 5103, 1455])).
% 1.44/1.66 tff(5105,plain,
% 1.44/1.66 (~r(elem!1, s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3015, 77, 5104, 26])).
% 1.44/1.66 tff(5106,plain,
% 1.44/1.66 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[4984, 77, 2235, 3952])).
% 1.44/1.66 tff(5107,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[226, 5106])).
% 1.44/1.66 tff(5108,plain,
% 1.44/1.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5006, 77, 2235, 3952])).
% 1.44/1.66 tff(5109,plain,
% 1.44/1.66 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[149, 5108])).
% 1.44/1.66 tff(5110,plain,
% 1.44/1.66 (~b(elem!1, s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2539, 5102, 5109, 5107])).
% 1.44/1.66 tff(5111,plain,
% 1.44/1.66 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5016, 2235, 3952])).
% 1.44/1.66 tff(5112,plain,
% 1.44/1.66 (~r(z, s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2243, 2235, 26])).
% 1.44/1.66 tff(5113,plain,
% 1.44/1.66 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[267, 21, 5112])).
% 1.44/1.66 tff(5114,plain,
% 1.44/1.66 (b(z, s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5113, 253])).
% 1.44/1.66 tff(5115,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5116,plain,
% 1.44/1.66 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5117,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5116])).
% 1.44/1.66 tff(5118,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5117, 5115])).
% 1.44/1.66 tff(5119,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5120,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 1.44/1.66 tff(5121,plain,
% 1.44/1.66 (~b(s(s(s(s(s(z))))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5120, 116, 4804, 5114, 5111])).
% 1.44/1.66 tff(5122,plain,
% 1.44/1.66 (r(s(s(s(s(s(z))))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[898, 21, 895, 5121])).
% 1.44/1.66 tff(5123,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5124,plain,
% 1.44/1.66 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5125,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5124])).
% 1.44/1.66 tff(5126,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5125, 5123])).
% 1.44/1.66 tff(5127,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5128,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5127, 5126])).
% 1.44/1.66 tff(5129,plain,
% 1.44/1.66 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5128, 77, 26, 5122])).
% 1.44/1.66 tff(5130,plain,
% 1.44/1.66 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 5129])).
% 1.44/1.66 tff(5131,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5132,plain,
% 1.44/1.66 (((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5133,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5132])).
% 1.44/1.66 tff(5134,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5133, 5131])).
% 1.44/1.66 tff(5135,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5136,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5135, 5134])).
% 1.44/1.66 tff(5137,plain,
% 1.44/1.66 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5136, 77, 5104, 5122])).
% 1.44/1.66 tff(5138,plain,
% 1.44/1.66 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[4222])).
% 1.44/1.66 tff(5139,plain,
% 1.44/1.66 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[466])).
% 1.44/1.66 tff(5140,plain,
% 1.44/1.66 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.44/1.66 inference(transitivity,[status(thm)],[5139, 4222])).
% 1.44/1.66 tff(5141,plain,
% 1.44/1.66 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5140, 5138])).
% 1.44/1.66 tff(5142,plain,
% 1.44/1.66 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5141])).
% 1.44/1.66 tff(5143,plain,
% 1.44/1.66 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[1901, 5142])).
% 1.44/1.66 tff(5144,assumption,(~r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.66 tff(5145,plain,
% 1.44/1.66 (((~![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)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5146,plain,
% 1.44/1.66 ((~![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)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5147,plain,
% 1.44/1.66 ((~![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))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5146, 5145])).
% 1.44/1.66 tff(5148,plain,
% 1.44/1.66 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5147, 21, 5144])).
% 1.44/1.66 tff(5149,plain,
% 1.44/1.66 (b(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5148, 5143])).
% 1.44/1.66 tff(5150,plain,
% 1.44/1.66 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1474])).
% 1.44/1.66 tff(5151,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.44/1.66 tff(5152,plain,
% 1.44/1.66 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5151, 5150])).
% 1.44/1.66 tff(5153,plain,
% 1.44/1.66 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1474])).
% 1.44/1.66 tff(5154,plain,
% 1.44/1.66 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[466])).
% 1.44/1.66 tff(5155,plain,
% 1.44/1.66 (~r(s(z), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2959, 466, 2956])).
% 1.44/1.66 tff(5156,plain,
% 1.44/1.66 (b(s(z), s(s(z)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[172, 5155])).
% 1.44/1.66 tff(5157,plain,
% 1.44/1.66 (b(elem!1, s(s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5156, 5154])).
% 1.44/1.66 tff(5158,plain,
% 1.44/1.66 (b(elem!1, s(elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5157, 5153])).
% 1.44/1.66 tff(5159,plain,
% 1.44/1.66 (b(s(elem!1), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1549, 466, 1331])).
% 1.44/1.66 tff(5160,plain,
% 1.44/1.66 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1476])).
% 1.44/1.66 tff(5161,plain,
% 1.44/1.66 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.44/1.66 inference(symmetry,[status(thm)],[5160])).
% 1.44/1.66 tff(5162,plain,
% 1.44/1.66 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3953, 5161])).
% 1.44/1.66 tff(5163,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5164,plain,
% 1.44/1.66 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5165,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5164])).
% 1.44/1.66 tff(5166,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5165, 5163])).
% 1.44/1.66 tff(5167,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5168,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5167, 5166])).
% 1.44/1.66 tff(5169,plain,
% 1.44/1.66 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5168, 77, 493, 429])).
% 1.44/1.66 tff(5170,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5169, 5162])).
% 1.44/1.66 tff(5171,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5172,plain,
% 1.44/1.66 (~r(elem!1, s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5171, 1533, 3953, 466])).
% 1.44/1.66 tff(5173,plain,
% 1.44/1.66 (b(elem!1, s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1892, 2008, 5172])).
% 1.44/1.66 tff(5174,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5175,plain,
% 1.44/1.66 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5176,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5175])).
% 1.44/1.66 tff(5177,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5176, 5174])).
% 1.44/1.66 tff(5178,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5179,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5178, 5177])).
% 1.44/1.66 tff(5180,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5179, 116, 5173, 5159, 5158, 5152, 5149])).
% 1.44/1.66 tff(5181,plain,((~(s(z) = elem!1)) | r(elem!1, s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5182,plain,
% 1.44/1.66 (~(s(z) = elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5181, 5137, 5130, 3952, 5110, 5102, 5105])).
% 1.44/1.66 tff(5183,plain,
% 1.44/1.66 (r(s(z), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[357, 5182, 340])).
% 1.44/1.66 tff(5184,plain,
% 1.44/1.66 (~r(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2815, 5183, 5104])).
% 1.44/1.66 tff(5185,plain,
% 1.44/1.66 (b(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[210, 5184])).
% 1.44/1.66 tff(5186,plain,
% 1.44/1.66 (~(z = elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[445, 5103])).
% 1.44/1.66 tff(5187,plain,
% 1.44/1.66 (b(s(s(elem!1)), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2832, 466, 2247])).
% 1.44/1.66 tff(5188,plain,
% 1.44/1.66 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[4763])).
% 1.44/1.66 tff(5189,plain,
% 1.44/1.66 (~r(z, s(s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2486, 5188])).
% 1.44/1.66 tff(5190,plain,
% 1.44/1.66 (b(z, s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[514, 5189])).
% 1.44/1.66 tff(5191,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5192,plain,
% 1.44/1.66 (((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(5193,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[5192])).
% 1.44/1.66 tff(5194,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[5193, 5191])).
% 1.44/1.66 tff(5195,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(5196,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[5195, 5194])).
% 1.44/1.66 tff(5197,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5196, 116, 1055, 668, 1879, 573])).
% 1.44/1.66 tff(5198,plain,((~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(5199,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[5198, 5190, 5173, 1055, 5187])).
% 1.44/1.66 tff(5200,plain,((~(s(z) = elem!1)) | (~b(z, elem!1)) | r(z, s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5201,plain,
% 1.44/1.67 (~(s(z) = elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5200, 1055, 2486, 3953, 1525, 2247])).
% 1.44/1.67 tff(5202,plain,
% 1.44/1.67 (~(elem!1 = s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[420, 5201])).
% 1.44/1.67 tff(5203,plain,
% 1.44/1.67 (r(s(z), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[357, 5201, 340])).
% 1.44/1.67 tff(5204,plain,
% 1.44/1.67 (~r(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2815, 5203, 575])).
% 1.44/1.67 tff(5205,plain,
% 1.44/1.67 (b(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[210, 5204])).
% 1.44/1.67 tff(5206,plain,
% 1.44/1.67 (~b(z, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3032, 5205, 2247, 1055, 1620, 575, 5202])).
% 1.44/1.67 tff(5207,plain,
% 1.44/1.67 (r(z, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[289, 5206])).
% 1.44/1.67 tff(5208,plain,
% 1.44/1.67 (~r(s(s(z)), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3659, 5207, 66])).
% 1.44/1.67 tff(5209,plain,
% 1.44/1.67 (b(s(s(z)), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[391, 21, 388, 5208])).
% 1.44/1.67 tff(5210,plain,
% 1.44/1.67 (~r(elem!1, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2095, 5207, 575])).
% 1.44/1.67 tff(5211,plain,
% 1.44/1.67 (b(elem!1, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[633, 5210, 5202])).
% 1.44/1.67 tff(5212,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5213,plain,
% 1.44/1.67 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5214,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5213])).
% 1.44/1.67 tff(5215,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5214, 5212])).
% 1.44/1.67 tff(5216,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5217,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5216, 5215])).
% 1.44/1.67 tff(5218,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5217, 116, 1055, 5205, 5211, 1331, 5209])).
% 1.44/1.67 tff(5219,plain,((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (elem!1 = s(s(s(z)))) | b(s(z), elem!1) | r(z, s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5220,plain,
% 1.44/1.67 (~b(z, elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5219, 5102, 5104, 26, 4804, 4805, 340, 5112, 3952, 5110])).
% 1.44/1.67 tff(5221,plain,
% 1.44/1.67 (r(z, elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1044, 5220, 5186])).
% 1.44/1.67 tff(5222,plain,
% 1.44/1.67 (~r(z, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3295, 5183, 5221])).
% 1.44/1.67 tff(5223,plain,
% 1.44/1.67 (b(z, s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[289, 5222])).
% 1.44/1.67 tff(5224,plain,
% 1.44/1.67 (~b(s(z), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3291, 5223, 4804, 5185])).
% 1.44/1.67 tff(5225,plain,
% 1.44/1.67 (r(s(z), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[194, 5224])).
% 1.44/1.67 tff(5226,plain,
% 1.44/1.67 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5227,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5226])).
% 1.44/1.67 tff(5228,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5227, 5009])).
% 1.44/1.67 tff(5229,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5230,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5229, 5228])).
% 1.44/1.67 tff(5231,plain,
% 1.44/1.67 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5230, 116, 5107, 5109, 5130])).
% 1.44/1.67 tff(5232,plain,
% 1.44/1.67 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1940, 21, 5231, 1708])).
% 1.44/1.67 tff(5233,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5234,plain,
% 1.44/1.67 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), 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)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5235,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5234])).
% 1.44/1.67 tff(5236,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5235, 5233])).
% 1.44/1.67 tff(5237,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5238,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5237, 5236])).
% 1.44/1.67 tff(5239,plain,
% 1.44/1.67 (~b(z, s(s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5238, 116, 4804, 5114, 5111])).
% 1.44/1.67 tff(5240,plain,
% 1.44/1.67 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3778, 21, 5239])).
% 1.44/1.67 tff(5241,plain,
% 1.44/1.67 (r(z, s(s(s(s(s(z))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5240, 3768])).
% 1.44/1.67 tff(5242,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5243,plain,
% 1.44/1.67 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5244,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5243])).
% 1.44/1.67 tff(5245,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5244, 5242])).
% 1.44/1.67 tff(5246,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5247,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5246, 5245])).
% 1.44/1.67 tff(5248,plain,
% 1.44/1.67 (~r(s(s(s(s(z)))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5247, 77, 5221, 5241, 5232])).
% 1.44/1.67 tff(5249,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[247, 5248])).
% 1.44/1.67 tff(5250,plain,
% 1.44/1.67 (~b(s(z), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[279, 5223, 5185, 5249])).
% 1.44/1.67 tff(5251,plain,
% 1.44/1.67 (r(s(z), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[325, 5250])).
% 1.44/1.67 tff(5252,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3975, 5251, 5225, 3952])).
% 1.44/1.67 tff(5253,plain,((~r(s(s(z)), s(s(s(z))))) | b(s(z), elem!1) | b(elem!1, z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5254,plain,
% 1.44/1.67 (~r(s(s(z)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5253, 1455, 340, 2])).
% 1.44/1.67 tff(5255,plain,
% 1.44/1.67 (b(s(s(z)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[105, 5254])).
% 1.44/1.67 tff(5256,plain,
% 1.44/1.67 (~(elem!1 = z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1680, 4966, 2])).
% 1.44/1.67 tff(5257,plain,
% 1.44/1.67 (r(elem!1, z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[545, 5256, 1455])).
% 1.44/1.67 tff(5258,plain,
% 1.44/1.67 (~r(elem!1, s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3015, 77, 5257, 26])).
% 1.44/1.67 tff(5259,plain,
% 1.44/1.67 (~(z = elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[445, 5256])).
% 1.44/1.67 tff(5260,plain,
% 1.44/1.67 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1474])).
% 1.44/1.67 tff(5261,plain,
% 1.44/1.67 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5260, 1820])).
% 1.44/1.67 tff(5262,plain,
% 1.44/1.67 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5261])).
% 1.44/1.67 tff(5263,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 1.44/1.67 tff(5264,plain,
% 1.44/1.67 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5263])).
% 1.44/1.67 tff(5265,plain,
% 1.44/1.67 (s(z) = s(elem!1)),
% 1.44/1.67 inference(transitivity,[status(thm)],[44, 5264, 520])).
% 1.44/1.67 tff(5266,plain,
% 1.44/1.67 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5265])).
% 1.44/1.67 tff(5267,plain,
% 1.44/1.67 (z = elem!1),
% 1.44/1.67 inference(transitivity,[status(thm)],[473, 5266, 460])).
% 1.44/1.67 tff(5268,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[518, 5267])).
% 1.44/1.67 tff(5269,plain,((~(s(s(z)) = s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5270,plain,
% 1.44/1.67 (~(s(s(z)) = s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5269, 518])).
% 1.44/1.67 tff(5271,plain,
% 1.44/1.67 (~(s(s(elem!1)) = s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5270, 5262])).
% 1.44/1.67 tff(5272,plain,
% 1.44/1.67 (~b(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1458, 466, 1455])).
% 1.44/1.67 tff(5273,plain,
% 1.44/1.67 (r(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[210, 5272])).
% 1.44/1.67 tff(5274,plain,
% 1.44/1.67 (~r(s(s(s(s(z)))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2285, 5273, 66])).
% 1.44/1.67 tff(5275,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[247, 5274])).
% 1.44/1.67 tff(5276,plain,
% 1.44/1.67 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5140])).
% 1.44/1.67 tff(5277,plain,
% 1.44/1.67 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1901, 5276])).
% 1.44/1.67 tff(5278,plain,
% 1.44/1.67 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2005])).
% 1.44/1.67 tff(5279,plain,
% 1.44/1.67 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[566, 5278])).
% 1.44/1.67 tff(5280,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3388, 116, 616, 1879, 846, 1878])).
% 1.44/1.67 tff(5281,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5282,plain,
% 1.44/1.67 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5281, 1879, 846, 1878])).
% 1.44/1.67 tff(5283,plain,
% 1.44/1.67 (r(s(s(elem!1)), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[743, 5282, 574])).
% 1.44/1.67 tff(5284,plain,
% 1.44/1.67 (~r(z, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3440, 5283, 448])).
% 1.44/1.67 tff(5285,plain,
% 1.44/1.67 (b(z, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[514, 5284])).
% 1.44/1.67 tff(5286,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5287,plain,
% 1.44/1.67 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5288,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5287])).
% 1.44/1.67 tff(5289,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5288, 5286])).
% 1.44/1.67 tff(5290,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5291,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 1.44/1.67 tff(5292,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5291, 116, 5285, 1879, 846, 573, 1878])).
% 1.44/1.67 tff(5293,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(5294,plain,
% 1.44/1.67 (~b(elem!1, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5293, 448, 573, 1878, 5159, 5279])).
% 1.44/1.67 tff(5295,plain,
% 1.44/1.67 (r(elem!1, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1892, 5294, 2008])).
% 1.44/1.67 tff(5296,plain,
% 1.44/1.67 (~r(z, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[502, 5295, 448])).
% 1.44/1.67 tff(5297,plain,
% 1.44/1.67 (b(z, s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[514, 5296])).
% 1.44/1.67 tff(5298,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.44/1.67 tff(5299,plain,
% 1.44/1.67 (b(elem!1, s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5298, 5153])).
% 1.44/1.67 tff(5300,plain,
% 1.44/1.67 (~r(elem!1, s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5171, 5295, 3953, 466])).
% 1.44/1.67 tff(5301,plain,
% 1.44/1.67 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3953, 4328])).
% 1.44/1.67 tff(5302,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5303,plain,
% 1.44/1.67 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5304,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5303])).
% 1.44/1.67 tff(5305,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5304, 5302])).
% 1.44/1.67 tff(5306,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5307,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5306, 5305])).
% 1.44/1.67 tff(5308,plain,
% 1.44/1.67 (~r(s(s(s(s(z)))), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5307, 77, 5295, 5301])).
% 1.44/1.67 tff(5309,plain,
% 1.44/1.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[4415, 5308, 1331, 5300, 1532])).
% 1.44/1.67 tff(5310,plain,
% 1.44/1.67 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[149, 5309])).
% 1.44/1.67 tff(5311,plain,
% 1.44/1.67 (r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5310, 1521])).
% 1.44/1.67 tff(5312,plain,
% 1.44/1.67 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[1578])).
% 1.44/1.67 tff(5313,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1475])).
% 1.44/1.67 tff(5314,plain,
% 1.44/1.67 (b(s(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)],[5313])).
% 1.44/1.67 tff(5315,plain,
% 1.44/1.67 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5314])).
% 1.44/1.67 tff(5316,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5317,plain,
% 1.44/1.67 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5318,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[5317])).
% 1.44/1.67 tff(5319,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[5318, 5316])).
% 1.44/1.67 tff(5320,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(5321,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5320, 5319])).
% 1.44/1.67 tff(5322,plain,
% 1.44/1.67 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[5321, 116, 5297, 573, 254])).
% 1.44/1.67 tff(5323,plain,
% 1.44/1.67 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5322, 5315])).
% 1.44/1.67 tff(5324,plain,
% 1.44/1.67 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1146, 5323])).
% 1.44/1.67 tff(5325,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[5324, 5312])).
% 1.44/1.67 tff(5326,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.44/1.67 tff(5327,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5328,plain,
% 1.44/1.67 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(5329,plain,
% 1.44/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5328])).
% 1.44/1.68 tff(5330,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5329, 5327])).
% 1.44/1.68 tff(5331,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5332,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5331, 5330])).
% 1.44/1.68 tff(5333,plain,
% 1.44/1.68 ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5332, 77, 5326, 5325])).
% 1.44/1.68 tff(5334,plain,
% 1.44/1.68 (~r(s(s(elem!1)), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5333, 5311])).
% 1.44/1.68 tff(5335,plain,
% 1.44/1.68 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[767, 5334, 760])).
% 1.44/1.68 tff(5336,plain,
% 1.44/1.68 (b(elem!1, s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1068, 5300, 1532])).
% 1.44/1.68 tff(5337,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5338,plain,
% 1.44/1.68 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5339,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5338])).
% 1.44/1.68 tff(5340,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5339, 5337])).
% 1.44/1.68 tff(5341,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5342,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5341, 5340])).
% 1.44/1.68 tff(5343,plain,
% 1.44/1.68 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5342, 116, 5336, 5159, 5335, 5299])).
% 1.44/1.68 tff(5344,plain,
% 1.44/1.68 (r(s(s(elem!1)), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[743, 5343, 5279])).
% 1.44/1.68 tff(5345,plain,
% 1.44/1.68 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1033, 5344, 448, 1508, 573, 5297])).
% 1.44/1.68 tff(5346,plain,
% 1.44/1.68 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[885, 5345, 5277])).
% 1.44/1.68 tff(5347,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1596, 5308, 1585])).
% 1.44/1.68 tff(5348,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5349,plain,
% 1.44/1.68 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5350,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5349])).
% 1.44/1.68 tff(5351,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5350, 5348])).
% 1.44/1.68 tff(5352,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, 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))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5353,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5352, 5351])).
% 1.44/1.68 tff(5354,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5353, 116, 5336, 254, 5347, 5346])).
% 1.44/1.68 tff(5355,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1940, 21, 5354, 1708])).
% 1.44/1.68 tff(5356,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5357,plain,
% 1.44/1.68 (((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5358,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5357])).
% 1.44/1.68 tff(5359,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5358, 5356])).
% 1.44/1.68 tff(5360,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5361,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5360, 5359])).
% 1.44/1.68 tff(5362,plain,
% 1.44/1.68 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5361, 116, 5336, 5159, 254, 5346])).
% 1.44/1.68 tff(5363,plain,
% 1.44/1.68 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1364, 1532])).
% 1.44/1.68 tff(5364,plain,
% 1.44/1.68 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[858, 21, 5363, 5362])).
% 1.44/1.68 tff(5365,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5366,plain,
% 1.44/1.68 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, 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(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5367,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5366])).
% 1.44/1.68 tff(5368,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5367, 5365])).
% 1.44/1.68 tff(5369,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5370,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5369, 5368])).
% 1.44/1.68 tff(5371,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5370, 116, 212, 1054, 1331, 5298])).
% 1.44/1.68 tff(5372,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(5373,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5372, 5336, 1331, 5298])).
% 1.44/1.68 tff(5374,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[226, 5373])).
% 1.44/1.68 tff(5375,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5374, 4253])).
% 1.44/1.68 tff(5376,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5377,plain,
% 1.44/1.68 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(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(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5378,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5377])).
% 1.44/1.68 tff(5379,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5378, 5376])).
% 1.44/1.68 tff(5380,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5381,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5380, 5379])).
% 1.44/1.68 tff(5382,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5381, 77, 5375, 5364, 5355])).
% 1.44/1.68 tff(5383,plain,((~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z)) | (~(s(z) = elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(5384,plain,
% 1.44/1.68 (~r(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5383, 5275, 5187, 5271, 1641, 466, 1331, 5157, 3953, 2011])).
% 1.44/1.68 tff(5385,plain,
% 1.44/1.68 (b(z, elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1044, 5384, 518])).
% 1.44/1.68 tff(5386,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5387,plain,
% 1.44/1.68 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5388,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5387])).
% 1.44/1.68 tff(5389,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5388, 5386])).
% 1.44/1.68 tff(5390,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5391,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5390, 5389])).
% 1.44/1.68 tff(5392,plain,
% 1.44/1.68 (~b(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5391, 116, 5385, 5159, 5158])).
% 1.44/1.68 tff(5393,plain,
% 1.44/1.68 (~b(z, s(s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5392, 1514])).
% 1.44/1.68 tff(5394,plain,
% 1.44/1.68 (r(z, s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1174, 5393])).
% 1.44/1.68 tff(5395,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5396,plain,
% 1.44/1.68 (((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(5397,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[5396])).
% 1.44/1.68 tff(5398,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[5397, 5395])).
% 1.44/1.68 tff(5399,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(5400,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5399, 5398])).
% 1.44/1.68 tff(5401,plain,
% 1.44/1.68 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5400, 116, 5385, 5187, 5275, 5158])).
% 1.44/1.68 tff(5402,plain,
% 1.44/1.68 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5401, 5315])).
% 1.44/1.68 tff(5403,plain,
% 1.44/1.68 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1146, 5402])).
% 1.44/1.68 tff(5404,plain,
% 1.44/1.68 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[5403, 5312])).
% 1.44/1.68 tff(5405,assumption,(r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.68 tff(5406,plain,
% 1.44/1.68 (~r(elem!1, s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[5171, 429, 3953, 466])).
% 1.44/1.68 tff(5407,plain,
% 1.44/1.68 (b(elem!1, s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1892, 5406, 2008])).
% 1.44/1.69 tff(5408,plain,
% 1.44/1.69 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5281, 5407, 846, 1878])).
% 1.44/1.69 tff(5409,plain,
% 1.44/1.69 (r(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[743, 5408, 5279])).
% 1.44/1.69 tff(5410,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[4284, 77, 5409, 429, 5405])).
% 1.44/1.69 tff(5411,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(5412,plain,
% 1.44/1.69 (~r(elem!1, s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5411, 5404, 5159, 2011, 3953, 466])).
% 1.44/1.69 tff(5413,plain,
% 1.44/1.69 (b(elem!1, s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1068, 5412, 1532])).
% 1.44/1.69 tff(5414,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5372, 5413, 1331, 5157])).
% 1.44/1.69 tff(5415,plain,
% 1.44/1.69 (r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[226, 5414])).
% 1.44/1.69 tff(5416,plain,
% 1.44/1.69 (~r(z, s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1572, 5415, 5394])).
% 1.44/1.69 tff(5417,plain,
% 1.44/1.69 (b(z, s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1576, 21, 5416, 1563])).
% 1.44/1.69 tff(5418,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5419,plain,
% 1.44/1.69 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5420,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[5419])).
% 1.44/1.69 tff(5421,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[5420, 5418])).
% 1.44/1.69 tff(5422,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(5423,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5422, 5421])).
% 1.44/1.69 tff(5424,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5423, 116, 5385, 5413, 5275, 5417])).
% 1.44/1.69 tff(5425,plain,((~(s(z) = elem!1)) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (z = elem!1) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | r(elem!1, s(s(z))) | (~b(s(s(s(z))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(5426,plain,
% 1.44/1.69 (~(s(z) = elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5425, 4966, 3952, 5259, 5255, 26, 5258, 4804, 1455])).
% 1.44/1.69 tff(5427,plain,
% 1.44/1.69 (r(s(z), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[357, 5426, 340])).
% 1.44/1.69 tff(5428,plain,
% 1.44/1.69 (~(elem!1 = s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[420, 5426])).
% 1.44/1.69 tff(5429,plain,
% 1.44/1.69 (~r(s(z), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2815, 5427, 5257])).
% 1.44/1.69 tff(5430,plain,
% 1.44/1.69 (b(s(z), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[210, 5429])).
% 1.44/1.69 tff(5431,plain,
% 1.44/1.69 (~r(z, elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3482, 5430, 340, 4804, 5255, 1455, 5256, 4966])).
% 1.44/1.69 tff(5432,plain,
% 1.44/1.69 (b(z, elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1044, 5431, 5259])).
% 1.44/1.69 tff(5433,plain,
% 1.44/1.69 (~b(z, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3032, 5432, 4804, 5430, 4805, 5257, 5428])).
% 1.44/1.69 tff(5434,plain,
% 1.44/1.69 (r(z, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[289, 5433])).
% 1.44/1.69 tff(5435,plain,
% 1.44/1.69 (~r(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2095, 5434, 5257])).
% 1.44/1.69 tff(5436,plain,
% 1.44/1.69 (b(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[633, 5435, 5428])).
% 1.44/1.69 tff(5437,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5438,plain,
% 1.44/1.69 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5439,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[5438])).
% 1.44/1.69 tff(5440,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[5439, 5437])).
% 1.44/1.69 tff(5441,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(5442,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5441, 5440])).
% 1.44/1.69 tff(5443,plain,
% 1.44/1.69 (~b(s(z), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5442, 116, 5432, 5430, 5436, 4804])).
% 1.44/1.69 tff(5444,plain,
% 1.44/1.69 (r(s(z), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[194, 5443])).
% 1.44/1.69 tff(5445,plain,
% 1.44/1.69 (~r(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[368, 5444, 5427])).
% 1.44/1.69 tff(5446,plain,
% 1.44/1.69 (b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1345, 5445, 4805])).
% 1.44/1.69 tff(5447,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5448,plain,
% 1.44/1.69 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5449,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[5448])).
% 1.44/1.69 tff(5450,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[5449, 5447])).
% 1.44/1.69 tff(5451,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(5452,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5451, 5450])).
% 1.44/1.69 tff(5453,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5452, 116, 5432, 4804, 5446, 5255, 4966])).
% 1.44/1.69 tff(5454,plain,(b(elem!1, z) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(5455,plain,
% 1.44/1.69 (b(elem!1, z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5454, 340, 2])).
% 1.44/1.69 tff(5456,plain,
% 1.44/1.69 (~r(z, elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[456, 428, 26])).
% 1.44/1.69 tff(5457,plain,
% 1.44/1.69 (elem!1 = s(s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[4888, 442, 360, 340, 2])).
% 1.44/1.69 tff(5458,plain,
% 1.44/1.69 (s(s(s(z))) = elem!1),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5457, 591])).
% 1.44/1.69 tff(5459,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1750, 5458])).
% 1.44/1.69 tff(5460,plain,((~(z = elem!1)) | (~r(s(z), elem!1)) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(5461,plain,
% 1.44/1.69 (~(z = elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5460, 360, 340, 2])).
% 1.44/1.69 tff(5462,plain,
% 1.44/1.69 (b(z, elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1044, 5461, 5456])).
% 1.44/1.69 tff(5463,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5464,plain,
% 1.44/1.69 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5465,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[5464])).
% 1.44/1.69 tff(5466,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[5465, 5463])).
% 1.44/1.69 tff(5467,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(5468,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5467, 5466])).
% 1.44/1.69 tff(5469,plain,
% 1.44/1.69 ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5468, 116])).
% 1.44/1.69 tff(5470,plain,
% 1.44/1.69 (~b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5469, 5462, 4804, 5455])).
% 1.44/1.69 tff(5471,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5472,plain,
% 1.44/1.69 (((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5473,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[5472])).
% 1.44/1.69 tff(5474,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[5473, 5471])).
% 1.44/1.69 tff(5475,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(5476,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5475, 5474])).
% 1.44/1.69 tff(5477,plain,
% 1.44/1.69 (~r(s(s(z)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5476, 77, 360, 428])).
% 1.44/1.69 tff(5478,plain,
% 1.44/1.69 (b(s(s(z)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[391, 21, 388, 5477])).
% 1.44/1.69 tff(5479,plain,
% 1.44/1.69 (~r(s(z), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[368, 359, 360])).
% 1.44/1.69 tff(5480,plain,
% 1.44/1.69 (b(s(z), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[194, 5479])).
% 1.44/1.69 tff(5481,plain,
% 1.44/1.69 (~r(s(s(z)), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5025, 359, 428])).
% 1.44/1.69 tff(5482,plain,
% 1.44/1.69 (b(s(s(z)), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[105, 5481])).
% 1.44/1.69 tff(5483,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5484,plain,
% 1.44/1.69 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5485,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[5484])).
% 1.44/1.69 tff(5486,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[5485, 5483])).
% 1.44/1.69 tff(5487,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(5488,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5487, 5486])).
% 1.44/1.69 tff(5489,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5488, 116, 1055, 2247, 5482, 5480, 5478])).
% 1.44/1.69 tff(5490,plain,((~r(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(5491,plain,
% 1.44/1.69 (~r(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5490, 5462, 4804, 360, 428])).
% 1.44/1.69 tff(5492,plain,
% 1.44/1.69 (elem!1 = s(s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1345, 5491, 5470])).
% 1.44/1.69 tff(5493,plain,
% 1.44/1.69 (s(s(s(z))) = elem!1),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5492, 591])).
% 1.44/1.69 tff(5494,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5495,plain,
% 1.44/1.69 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5496,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[5495])).
% 1.44/1.69 tff(5497,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[5496, 5494])).
% 1.44/1.69 tff(5498,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(5499,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[5498, 5497])).
% 1.44/1.69 tff(5500,plain,
% 1.44/1.69 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[5499, 77, 360, 3953, 2418])).
% 1.44/1.69 tff(5501,plain,
% 1.44/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[323, 21, 320, 5500])).
% 1.44/1.69 tff(5502,plain,
% 1.44/1.69 (~r(s(z), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[4008, 428, 360])).
% 1.44/1.69 tff(5503,plain,
% 1.44/1.69 (b(s(z), s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[170, 21, 54, 5502])).
% 1.44/1.69 tff(5504,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5505,plain,
% 1.44/1.69 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(5506,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[5505])).
% 1.44/1.70 tff(5507,plain,
% 1.44/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.70 inference(transitivity,[status(thm)],[5506, 5504])).
% 1.44/1.70 tff(5508,plain,
% 1.44/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.44/1.70 inference(quant_inst,[status(thm)],[])).
% 1.44/1.70 tff(5509,plain,
% 1.44/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[5508, 5507])).
% 1.44/1.70 tff(5510,plain,
% 1.44/1.70 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[5509, 77, 428, 3953, 2418])).
% 1.44/1.70 tff(5511,plain,
% 1.44/1.70 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[149, 5510])).
% 1.44/1.70 tff(5512,plain,
% 1.44/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(5513,plain,
% 1.44/1.70 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(5514,plain,
% 1.44/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[5513])).
% 1.44/1.70 tff(5515,plain,
% 1.44/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.70 inference(transitivity,[status(thm)],[5514, 5512])).
% 1.44/1.70 tff(5516,plain,
% 1.44/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.44/1.70 inference(quant_inst,[status(thm)],[])).
% 1.44/1.70 tff(5517,plain,
% 1.44/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[5516, 5515])).
% 1.44/1.70 tff(5518,plain,
% 1.44/1.70 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[5517, 77, 428, 2418])).
% 1.44/1.70 tff(5519,plain,
% 1.44/1.70 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[226, 5518])).
% 1.44/1.70 tff(5520,plain,
% 1.44/1.70 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5521,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5520])).
% 1.54/1.70 tff(5522,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5521, 3514])).
% 1.54/1.70 tff(5523,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(5524,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5523, 5522])).
% 1.54/1.70 tff(5525,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5524, 116, 5519, 5511, 5503, 5501])).
% 1.54/1.70 tff(5526,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(5527,plain,
% 1.54/1.70 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5526, 360, 3952, 428])).
% 1.54/1.70 tff(5528,plain,
% 1.54/1.70 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4113, 5491, 3946])).
% 1.54/1.70 tff(5529,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1596, 5528, 5527])).
% 1.54/1.70 tff(5530,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[1746])).
% 1.54/1.70 tff(5531,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[5530])).
% 1.54/1.70 tff(5532,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[1725, 5531])).
% 1.54/1.70 tff(5533,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3986, 5532])).
% 1.54/1.70 tff(5534,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(5535,plain,
% 1.54/1.70 (~(s(s(s(z))) = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5534, 5529, 3946])).
% 1.54/1.70 tff(5536,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5535, 5493])).
% 1.54/1.70 tff(5537,plain,((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(5538,plain,
% 1.54/1.70 (~r(s(z), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5537, 428, 340, 2])).
% 1.54/1.70 tff(5539,plain,
% 1.54/1.70 (s(z) = elem!1),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[357, 5538, 340])).
% 1.54/1.70 tff(5540,plain,
% 1.54/1.70 (s(s(z)) = s(elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5539])).
% 1.54/1.70 tff(5541,plain,
% 1.54/1.70 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5540])).
% 1.54/1.70 tff(5542,plain,
% 1.54/1.70 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5541])).
% 1.54/1.70 tff(5543,plain,
% 1.54/1.70 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5539])).
% 1.54/1.70 tff(5544,plain,
% 1.54/1.70 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.54/1.70 inference(transitivity,[status(thm)],[5543, 4222])).
% 1.54/1.70 tff(5545,plain,
% 1.54/1.70 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5544])).
% 1.54/1.70 tff(5546,plain,
% 1.54/1.70 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[1901, 5545])).
% 1.54/1.70 tff(5547,plain,
% 1.54/1.70 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5541])).
% 1.54/1.70 tff(5548,plain,
% 1.54/1.70 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5547])).
% 1.54/1.70 tff(5549,plain,
% 1.54/1.70 (elem!1 = s(z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1984, 5539])).
% 1.54/1.70 tff(5550,plain,
% 1.54/1.70 (b(s(z), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1992, 5549, 5455])).
% 1.54/1.70 tff(5551,plain,
% 1.54/1.70 (~(elem!1 = z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[409, 5550, 340])).
% 1.54/1.70 tff(5552,plain,
% 1.54/1.70 (~(z = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[445, 5551])).
% 1.54/1.70 tff(5553,plain,
% 1.54/1.70 (b(z, elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1044, 5552, 5456])).
% 1.54/1.70 tff(5554,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5555,plain,
% 1.54/1.70 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5556,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5555])).
% 1.54/1.70 tff(5557,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5556, 5554])).
% 1.54/1.70 tff(5558,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(5559,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 1.54/1.70 tff(5560,plain,
% 1.54/1.70 ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5559, 116])).
% 1.54/1.70 tff(5561,plain,
% 1.54/1.70 (~b(s(s(s(z))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5560, 5553, 4804, 5455])).
% 1.54/1.70 tff(5562,plain,
% 1.54/1.70 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5561, 5548])).
% 1.54/1.70 tff(5563,plain,
% 1.54/1.70 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5539])).
% 1.54/1.70 tff(5564,plain,
% 1.54/1.70 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5563])).
% 1.54/1.70 tff(5565,plain,
% 1.54/1.70 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[566, 5564])).
% 1.54/1.70 tff(5566,plain,
% 1.54/1.70 (r(s(s(elem!1)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[743, 5565, 5562])).
% 1.54/1.70 tff(5567,plain,
% 1.54/1.70 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5540])).
% 1.54/1.70 tff(5568,plain,
% 1.54/1.70 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5567, 1820])).
% 1.54/1.70 tff(5569,plain,
% 1.54/1.70 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5568])).
% 1.54/1.70 tff(5570,plain,
% 1.54/1.70 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5269, 5552])).
% 1.54/1.70 tff(5571,plain,
% 1.54/1.70 (~(s(s(elem!1)) = s(elem!1))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5570, 5569])).
% 1.54/1.70 tff(5572,plain,
% 1.54/1.70 (~r(s(s(elem!1)), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2865, 5566, 428, 5539])).
% 1.54/1.70 tff(5573,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(elem!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[767, 5572, 5571])).
% 1.54/1.70 tff(5574,plain,
% 1.54/1.70 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5541])).
% 1.54/1.70 tff(5575,plain,
% 1.54/1.70 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5574, 1504])).
% 1.54/1.70 tff(5576,plain,
% 1.54/1.70 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5575])).
% 1.54/1.70 tff(5577,plain,
% 1.54/1.70 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[1138, 5576])).
% 1.54/1.70 tff(5578,plain,
% 1.54/1.70 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1531, 5539])).
% 1.54/1.70 tff(5579,plain,
% 1.54/1.70 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1364, 5578])).
% 1.54/1.70 tff(5580,plain,
% 1.54/1.70 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5540])).
% 1.54/1.70 tff(5581,plain,
% 1.54/1.70 (r(s(elem!1), elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[428, 5580])).
% 1.54/1.70 tff(5582,plain,
% 1.54/1.70 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5540, 5541])).
% 1.54/1.70 tff(5583,plain,
% 1.54/1.70 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5539])).
% 1.54/1.70 tff(5584,plain,
% 1.54/1.70 (b(z, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4796, 5553, 5539])).
% 1.54/1.70 tff(5585,plain,
% 1.54/1.70 (~b(s(z), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3291, 5584, 4804, 5550])).
% 1.54/1.70 tff(5586,plain,
% 1.54/1.70 (r(s(z), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[194, 5585])).
% 1.54/1.70 tff(5587,plain,
% 1.54/1.70 (r(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5586, 5583])).
% 1.54/1.70 tff(5588,plain,
% 1.54/1.70 (~r(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5025, 5587, 428])).
% 1.54/1.70 tff(5589,plain,
% 1.54/1.70 (b(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[105, 5588])).
% 1.54/1.70 tff(5590,plain,
% 1.54/1.70 (b(s(elem!1), s(s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5589, 5582])).
% 1.54/1.70 tff(5591,plain,
% 1.54/1.70 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4838, 5590, 5581, 5579, 5577, 5573, 5566])).
% 1.54/1.70 tff(5592,plain,
% 1.54/1.70 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[885, 5591, 5546])).
% 1.54/1.70 tff(5593,plain,
% 1.54/1.70 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1584, 5578])).
% 1.54/1.70 tff(5594,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5541])).
% 1.54/1.70 tff(5595,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3952, 5594])).
% 1.54/1.70 tff(5596,plain,
% 1.54/1.70 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[5541])).
% 1.54/1.70 tff(5597,plain,
% 1.54/1.70 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5596])).
% 1.54/1.70 tff(5598,plain,
% 1.54/1.70 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[5597])).
% 1.54/1.70 tff(5599,plain,
% 1.54/1.70 (r(elem!1, s(s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5587, 5598])).
% 1.54/1.70 tff(5600,plain,
% 1.54/1.70 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5307, 77, 5599, 5595])).
% 1.54/1.70 tff(5601,plain,
% 1.54/1.70 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1596, 5600, 5593])).
% 1.54/1.70 tff(5602,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, 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))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5603,plain,
% 1.54/1.70 (((~b(z, elem!1)) | (~b(elem!1, 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)))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, 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))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5604,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, 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)))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5603])).
% 1.54/1.70 tff(5605,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, 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))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5604, 5602])).
% 1.54/1.70 tff(5606,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(5607,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, 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)))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5606, 5605])).
% 1.54/1.70 tff(5608,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5607, 116, 5553, 5455, 5601, 5592])).
% 1.54/1.70 tff(5609,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)],[4691, 5608, 3952])).
% 1.54/1.70 tff(5610,plain,
% 1.54/1.70 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5609, 5542])).
% 1.54/1.70 tff(5611,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5612,plain,
% 1.54/1.70 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5613,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5612])).
% 1.54/1.70 tff(5614,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5613, 5611])).
% 1.54/1.70 tff(5615,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(5616,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5615, 5614])).
% 1.54/1.70 tff(5617,plain,
% 1.54/1.70 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5616, 116, 5590, 5573, 5610])).
% 1.54/1.70 tff(5618,plain,
% 1.54/1.70 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[858, 21, 5579, 5617])).
% 1.54/1.70 tff(5619,plain,
% 1.54/1.70 (~b(s(s(s(s(s(z))))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4300, 116, 5553, 5455, 5592])).
% 1.54/1.70 tff(5620,plain,
% 1.54/1.70 (r(s(s(s(s(s(z))))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[898, 21, 895, 5619])).
% 1.54/1.70 tff(5621,plain,
% 1.54/1.70 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5540])).
% 1.54/1.70 tff(5622,plain,
% 1.54/1.70 (r(s(elem!1), z)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[26, 5621])).
% 1.54/1.70 tff(5623,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4643, 77, 5622, 5620, 5618])).
% 1.54/1.70 tff(5624,plain,((~r(s(s(z)), elem!1)) | b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(5625,plain,
% 1.54/1.70 (~r(s(s(z)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5624, 340, 2])).
% 1.54/1.70 tff(5626,plain,
% 1.54/1.70 (~(elem!1 = z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1685, 5625, 2])).
% 1.54/1.70 tff(5627,plain,
% 1.54/1.70 (~(z = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[445, 5626])).
% 1.54/1.70 tff(5628,plain,
% 1.54/1.70 (~(s(s(z)) = elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[540, 5455, 2])).
% 1.54/1.70 tff(5629,plain,
% 1.54/1.70 (b(s(s(z)), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[426, 5625, 5628])).
% 1.54/1.70 tff(5630,plain,
% 1.54/1.70 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[1475])).
% 1.54/1.70 tff(5631,plain,
% 1.54/1.70 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[466])).
% 1.54/1.70 tff(5632,plain,
% 1.54/1.70 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5631, 5630])).
% 1.54/1.70 tff(5633,plain,
% 1.54/1.70 (b(s(z), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1992, 1985, 537])).
% 1.54/1.70 tff(5634,plain,
% 1.54/1.70 (b(z, elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1044, 1052, 518])).
% 1.54/1.70 tff(5635,plain,
% 1.54/1.70 (b(z, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[4796, 5634, 466])).
% 1.54/1.70 tff(5636,plain,
% 1.54/1.70 (~b(s(z), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3291, 5635, 2247, 270])).
% 1.54/1.70 tff(5637,plain,
% 1.54/1.70 (r(s(z), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[194, 5636])).
% 1.54/1.70 tff(5638,plain,
% 1.54/1.70 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3975, 5637, 3953])).
% 1.54/1.70 tff(5639,plain,
% 1.54/1.70 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[325, 5638])).
% 1.54/1.70 tff(5640,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1980, 5639, 466, 1052, 270])).
% 1.54/1.70 tff(5641,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[247, 5640])).
% 1.54/1.70 tff(5642,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5643,plain,
% 1.54/1.70 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(5644,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[5643])).
% 1.54/1.70 tff(5645,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[5644, 5642])).
% 1.54/1.70 tff(5646,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(5647,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[5646, 5645])).
% 1.54/1.70 tff(5648,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5647, 77, 3953, 228, 291])).
% 1.54/1.70 tff(5649,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(5650,plain,
% 1.54/1.70 (~r(z, s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[5649, 5641, 3953])).
% 1.54/1.70 tff(5651,plain,
% 1.54/1.70 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[1512])).
% 1.54/1.70 tff(5652,plain,
% 1.54/1.70 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[5651])).
% 1.54/1.70 tff(5653,assumption,(~(s(s(z)) = s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.70 tff(5654,plain,
% 1.54/1.70 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[1520])).
% 1.54/1.71 tff(5655,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5656,plain,
% 1.54/1.71 (((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5657,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5656])).
% 1.54/1.71 tff(5658,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[5657, 5655])).
% 1.54/1.71 tff(5659,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(5660,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5659, 5658])).
% 1.54/1.71 tff(5661,plain,
% 1.54/1.71 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5660, 77, 5326, 228])).
% 1.54/1.71 tff(5662,plain,
% 1.54/1.71 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5661, 5654])).
% 1.54/1.71 tff(5663,plain,
% 1.54/1.71 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[148, 5662, 5653])).
% 1.54/1.71 tff(5664,plain,
% 1.54/1.71 (b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5663, 5652])).
% 1.54/1.71 tff(5665,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1512])).
% 1.54/1.71 tff(5666,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[5665])).
% 1.54/1.71 tff(5667,plain,
% 1.54/1.71 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[138])).
% 1.54/1.71 tff(5668,plain,
% 1.54/1.71 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5653, 5667])).
% 1.54/1.71 tff(5669,plain,
% 1.54/1.71 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4252])).
% 1.54/1.71 tff(5670,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5671,plain,
% 1.54/1.71 (((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5672,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5671])).
% 1.54/1.71 tff(5673,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[5672, 5670])).
% 1.54/1.71 tff(5674,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(5675,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5674, 5673])).
% 1.54/1.71 tff(5676,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5675, 77, 5326, 228])).
% 1.54/1.71 tff(5677,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5676, 5669])).
% 1.54/1.71 tff(5678,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[225, 5677, 5668])).
% 1.54/1.71 tff(5679,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5678, 5666])).
% 1.54/1.71 tff(5680,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5681,plain,
% 1.54/1.71 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5682,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5681])).
% 1.54/1.71 tff(5683,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[5682, 5680])).
% 1.54/1.71 tff(5684,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(5685,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5684, 5683])).
% 1.54/1.71 tff(5686,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5685, 116, 1054, 846, 5679, 5664])).
% 1.54/1.71 tff(5687,plain,((~r(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (s(s(z)) = s(s(s(s(z))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(5688,plain,
% 1.54/1.71 ((~r(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~r(s(elem!1), z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5687, 144])).
% 1.54/1.71 tff(5689,plain,
% 1.54/1.71 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5688, 5641, 466, 846, 5326])).
% 1.54/1.71 tff(5690,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5200, 5689, 5650, 466, 3953, 5634, 2247])).
% 1.54/1.71 tff(5691,plain,(r(z, elem!1) | (~(s(z) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(s(z), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(5692,plain,
% 1.54/1.71 (r(z, elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5691, 466, 3953, 2247, 5159, 1641, 5633, 518])).
% 1.54/1.71 tff(5693,plain,
% 1.54/1.71 (r(z, s(z)) <=> r(z, elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[466])).
% 1.54/1.71 tff(5694,plain,
% 1.54/1.71 (r(z, elem!1) <=> r(z, s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[5693])).
% 1.54/1.71 tff(5695,plain,
% 1.54/1.71 (r(z, s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[448, 5694])).
% 1.54/1.71 tff(5696,assumption,(r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.71 tff(5697,plain,
% 1.54/1.71 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[466])).
% 1.54/1.71 tff(5698,plain,
% 1.54/1.71 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[5697, 1619])).
% 1.54/1.71 tff(5699,plain,
% 1.54/1.71 (r(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[292, 5698])).
% 1.54/1.71 tff(5700,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5307, 77, 5699, 5696])).
% 1.54/1.71 tff(5701,plain,
% 1.54/1.71 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3343, 5700, 340, 537, 1331, 5695, 292, 448])).
% 1.54/1.71 tff(5702,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[226, 5701])).
% 1.54/1.71 tff(5703,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5702, 4253])).
% 1.54/1.71 tff(5704,plain,
% 1.54/1.71 (~r(z, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[502, 5699, 448])).
% 1.54/1.71 tff(5705,plain,
% 1.54/1.71 (b(z, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[514, 5704])).
% 1.54/1.71 tff(5706,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5707,plain,
% 1.54/1.71 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5708,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5707])).
% 1.54/1.71 tff(5709,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[5708, 5706])).
% 1.54/1.71 tff(5710,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(5711,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5710, 5709])).
% 1.54/1.71 tff(5712,plain,
% 1.54/1.71 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5711, 116, 537, 5705, 573])).
% 1.54/1.71 tff(5713,plain,
% 1.54/1.71 (r(s(s(elem!1)), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[743, 5712, 5279])).
% 1.54/1.71 tff(5714,plain,
% 1.54/1.71 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1033, 5713, 448, 1508, 573, 5705])).
% 1.54/1.71 tff(5715,plain,
% 1.54/1.71 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[885, 5714, 5277])).
% 1.54/1.71 tff(5716,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1596, 5700, 1585])).
% 1.54/1.71 tff(5717,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, 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))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5718,plain,
% 1.54/1.71 (((~b(z, s(s(elem!1)))) | (~b(elem!1, 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)))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, 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))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5719,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, 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)))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5718])).
% 1.54/1.71 tff(5720,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, 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))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[5719, 5717])).
% 1.54/1.71 tff(5721,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, 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))))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(5722,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, 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)))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5721, 5720])).
% 1.54/1.71 tff(5723,plain,
% 1.54/1.71 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5722, 116, 537, 5705, 5716, 5715])).
% 1.54/1.71 tff(5724,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1940, 21, 5723, 1708])).
% 1.54/1.71 tff(5725,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5726,plain,
% 1.54/1.71 (((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5727,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5726])).
% 1.54/1.71 tff(5728,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[5727, 5725])).
% 1.54/1.71 tff(5729,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(5730,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 1.54/1.71 tff(5731,plain,
% 1.54/1.71 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5730, 116, 537, 5705, 5159, 5715])).
% 1.54/1.71 tff(5732,plain,
% 1.54/1.71 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[858, 21, 5363, 5731])).
% 1.54/1.71 tff(5733,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5381, 77, 5732, 5724])).
% 1.54/1.71 tff(5734,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5733, 5703])).
% 1.54/1.71 tff(5735,plain,((~r(s(z), s(s(s(z))))) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~b(s(s(elem!1)), z)) | b(s(z), elem!1) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(5736,plain,
% 1.54/1.71 (~r(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5735, 466, 537, 5692, 5187, 340, 1331, 5301])).
% 1.54/1.71 tff(5737,plain,
% 1.54/1.71 (b(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[194, 5736])).
% 1.54/1.71 tff(5738,plain,
% 1.54/1.71 (b(elem!1, s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5737, 5632])).
% 1.54/1.71 tff(5739,plain,
% 1.54/1.71 (~b(s(elem!1), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5293, 5738, 5187, 5692, 5159, 5279])).
% 1.54/1.71 tff(5740,plain,
% 1.54/1.71 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[4763])).
% 1.54/1.71 tff(5741,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.71 tff(5742,plain,
% 1.54/1.71 (~b(z, s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5741, 2968])).
% 1.54/1.71 tff(5743,plain,
% 1.54/1.71 (r(z, s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[514, 5742])).
% 1.54/1.71 tff(5744,plain,
% 1.54/1.71 (r(z, s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5743, 5740])).
% 1.54/1.71 tff(5745,plain,
% 1.54/1.71 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[2010])).
% 1.54/1.71 tff(5746,plain,
% 1.54/1.71 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5745])).
% 1.54/1.71 tff(5747,plain,
% 1.54/1.71 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4148, 5746])).
% 1.54/1.71 tff(5748,plain,
% 1.54/1.71 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[105, 5747])).
% 1.54/1.71 tff(5749,plain,
% 1.54/1.71 (~r(z, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2243, 5748, 66])).
% 1.54/1.71 tff(5750,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5749, 5744])).
% 1.54/1.71 tff(5751,plain,(b(z, s(s(s(z)))) | (~(s(z) = elem!1)) | (~r(s(s(z)), z)) | b(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(5752,plain,
% 1.54/1.71 (b(z, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[5751, 466, 66, 5739])).
% 1.54/1.71 tff(5753,plain,
% 1.54/1.71 (b(z, s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[5752, 2967])).
% 1.54/1.71 tff(5754,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5755,plain,
% 1.54/1.71 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(5756,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[5755])).
% 1.54/1.71 tff(5757,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[5756, 5754])).
% 1.54/1.72 tff(5758,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5759,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5758, 5757])).
% 1.54/1.72 tff(5760,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5759, 116, 537, 5753, 5738, 5187])).
% 1.54/1.72 tff(5761,plain,((~(s(z) = elem!1)) | (~b(elem!1, z)) | (~r(s(s(z)), z)) | b(s(z), elem!1) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(5762,plain,
% 1.54/1.72 (~(s(z) = elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5761, 5455, 26, 340, 5629, 3952, 4804, 5627])).
% 1.54/1.72 tff(5763,plain,
% 1.54/1.72 (r(s(z), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[357, 5762, 340])).
% 1.54/1.72 tff(5764,plain,
% 1.54/1.72 (b(z, elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1044, 1052, 446])).
% 1.54/1.72 tff(5765,plain,
% 1.54/1.72 (~b(elem!1, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5469, 5764, 2247, 537])).
% 1.54/1.72 tff(5766,plain,
% 1.54/1.72 (~(s(z) = elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5761, 537, 66, 340, 1331, 3953, 2247, 446])).
% 1.54/1.72 tff(5767,plain,
% 1.54/1.72 (r(s(z), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[357, 5766, 340])).
% 1.54/1.72 tff(5768,plain,
% 1.54/1.72 (~r(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2285, 155, 66])).
% 1.54/1.72 tff(5769,plain,
% 1.54/1.72 (b(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[247, 5768])).
% 1.54/1.72 tff(5770,plain,
% 1.54/1.72 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1063, 5769, 537, 5764])).
% 1.54/1.72 tff(5771,plain,
% 1.54/1.72 (~b(s(s(s(z))), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5560, 5764, 2247, 537])).
% 1.54/1.72 tff(5772,plain,
% 1.54/1.72 (~(elem!1 = s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3980, 175, 340])).
% 1.54/1.72 tff(5773,plain,
% 1.54/1.72 (r(elem!1, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1345, 5772, 1355])).
% 1.54/1.72 tff(5774,plain,
% 1.54/1.72 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4401, 77, 3953, 5773])).
% 1.54/1.72 tff(5775,plain,
% 1.54/1.72 (elem!1 = s(s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1068, 5774, 1525])).
% 1.54/1.72 tff(5776,plain,
% 1.54/1.72 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5775])).
% 1.54/1.72 tff(5777,plain,
% 1.54/1.72 (b(z, s(s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[1055, 5776])).
% 1.54/1.72 tff(5778,plain,
% 1.54/1.72 (~b(s(s(s(s(s(z))))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4883, 5777, 2247, 5769, 3953])).
% 1.54/1.72 tff(5779,plain,
% 1.54/1.72 (r(s(s(s(s(s(z))))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[898, 21, 895, 5778])).
% 1.54/1.72 tff(5780,plain,
% 1.54/1.72 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.54/1.72 inference(commutativity,[status(thm)],[])).
% 1.54/1.72 tff(5781,plain,
% 1.54/1.72 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.54/1.72 inference(symmetry,[status(thm)],[5780])).
% 1.54/1.72 tff(5782,plain,
% 1.54/1.72 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(z)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5781])).
% 1.54/1.72 tff(5783,plain,
% 1.54/1.72 (~(s(s(s(s(s(z))))) = s(z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[1901, 5782])).
% 1.54/1.72 tff(5784,plain,
% 1.54/1.72 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4700, 5775, 340])).
% 1.54/1.72 tff(5785,plain,
% 1.54/1.72 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[325, 5784])).
% 1.54/1.72 tff(5786,plain,
% 1.54/1.72 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5775])).
% 1.54/1.72 tff(5787,plain,
% 1.54/1.72 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5786])).
% 1.54/1.72 tff(5788,plain,
% 1.54/1.72 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[2720, 5787])).
% 1.54/1.72 tff(5789,plain,
% 1.54/1.72 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1146, 5788])).
% 1.54/1.72 tff(5790,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5791,plain,
% 1.54/1.72 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5792,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5791])).
% 1.54/1.72 tff(5793,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[5792, 5790])).
% 1.54/1.72 tff(5794,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5795,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5794, 5793])).
% 1.54/1.72 tff(5796,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5795, 77, 155, 5789, 5785])).
% 1.54/1.72 tff(5797,plain,
% 1.54/1.72 (b(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[402, 21, 135, 5796])).
% 1.54/1.72 tff(5798,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5799,plain,
% 1.54/1.72 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5800,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5799])).
% 1.54/1.72 tff(5801,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[5800, 5798])).
% 1.54/1.72 tff(5802,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5803,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5802, 5801])).
% 1.54/1.72 tff(5804,plain,
% 1.54/1.72 (~b(s(s(z)), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5803, 116, 2247, 175, 4978, 5797])).
% 1.54/1.72 tff(5805,plain,
% 1.54/1.72 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[105, 5804])).
% 1.54/1.72 tff(5806,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5016, 5805, 3953])).
% 1.54/1.72 tff(5807,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(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))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5808,plain,
% 1.54/1.72 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(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))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5809,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(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)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5808])).
% 1.54/1.72 tff(5810,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(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))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[5809, 5807])).
% 1.54/1.72 tff(5811,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5812,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(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)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5811, 5810])).
% 1.54/1.72 tff(5813,plain,
% 1.54/1.72 (~b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5812, 116, 2247, 175, 5806, 5777])).
% 1.54/1.72 tff(5814,plain,
% 1.54/1.72 (((~![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)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5815,plain,
% 1.54/1.72 ((~![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)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5816,plain,
% 1.54/1.72 ((~![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))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5815, 5814])).
% 1.54/1.72 tff(5817,plain,
% 1.54/1.72 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5816, 21, 5813])).
% 1.54/1.72 tff(5818,plain,
% 1.54/1.72 (r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5817, 5783])).
% 1.54/1.72 tff(5819,plain,
% 1.54/1.72 (~r(z, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2243, 5805, 66])).
% 1.54/1.72 tff(5820,plain,
% 1.54/1.72 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[267, 21, 5819])).
% 1.54/1.72 tff(5821,plain,
% 1.54/1.72 (b(z, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5820, 253])).
% 1.54/1.72 tff(5822,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5823,plain,
% 1.54/1.72 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5824,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5823])).
% 1.54/1.72 tff(5825,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[5824, 5822])).
% 1.54/1.72 tff(5826,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5827,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5826, 5825])).
% 1.54/1.72 tff(5828,plain,
% 1.54/1.72 (~b(z, s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5827, 116, 2247, 5821, 175])).
% 1.54/1.72 tff(5829,plain,
% 1.54/1.72 (r(z, s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[289, 5828])).
% 1.54/1.72 tff(5830,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5831,plain,
% 1.54/1.72 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5832,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5831])).
% 1.54/1.72 tff(5833,plain,
% 1.54/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[5832, 5830])).
% 1.54/1.72 tff(5834,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5835,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5834, 5833])).
% 1.54/1.72 tff(5836,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5835, 77, 5829, 5818, 5779])).
% 1.54/1.72 tff(5837,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | b(s(s(s(z))), elem!1) | (~b(z, elem!1)) | b(s(z), elem!1) | b(elem!1, s(s(s(s(z))))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(5838,plain,
% 1.54/1.72 (~b(s(z), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5837, 155, 3953, 66, 2247, 5771, 5764, 340, 5770, 5765])).
% 1.54/1.72 tff(5839,plain,
% 1.54/1.72 (r(s(z), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[194, 5838])).
% 1.54/1.72 tff(5840,plain,
% 1.54/1.72 (~r(elem!1, s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[368, 5839, 5767])).
% 1.54/1.72 tff(5841,plain,
% 1.54/1.72 (elem!1 = s(s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1345, 5840, 5765])).
% 1.54/1.72 tff(5842,plain,
% 1.54/1.72 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5841])).
% 1.54/1.72 tff(5843,plain,
% 1.54/1.72 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.54/1.72 inference(symmetry,[status(thm)],[5842])).
% 1.54/1.72 tff(5844,plain,
% 1.54/1.72 (s(elem!1) = s(s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5841])).
% 1.54/1.72 tff(5845,plain,
% 1.54/1.72 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5844])).
% 1.54/1.72 tff(5846,plain,
% 1.54/1.72 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5845])).
% 1.54/1.72 tff(5847,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[5846])).
% 1.54/1.72 tff(5848,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.54/1.72 inference(transitivity,[status(thm)],[5847, 5843])).
% 1.54/1.72 tff(5849,plain,
% 1.54/1.72 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5848])).
% 1.54/1.72 tff(5850,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5851,plain,
% 1.54/1.72 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5852,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5851])).
% 1.54/1.72 tff(5853,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[5852, 5850])).
% 1.54/1.72 tff(5854,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(5855,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[5854, 5853])).
% 1.54/1.72 tff(5856,plain,
% 1.54/1.72 (~b(z, s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5855, 116, 5764, 537, 1331])).
% 1.54/1.72 tff(5857,plain,
% 1.54/1.72 (r(z, s(s(z)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1174, 5856])).
% 1.54/1.72 tff(5858,plain,
% 1.54/1.72 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4668, 77, 3953, 5839])).
% 1.54/1.72 tff(5859,plain,
% 1.54/1.72 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2054, 21, 5858])).
% 1.54/1.72 tff(5860,plain,
% 1.54/1.72 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[5859, 2044])).
% 1.54/1.72 tff(5861,plain,
% 1.54/1.72 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[5841])).
% 1.54/1.72 tff(5862,plain,
% 1.54/1.72 (b(s(s(z)), s(s(s(z))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[1331, 5861])).
% 1.54/1.72 tff(5863,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(5864,plain,
% 1.54/1.72 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5865,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5864])).
% 1.54/1.73 tff(5866,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5865, 5863])).
% 1.54/1.73 tff(5867,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5868,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5867, 5866])).
% 1.54/1.73 tff(5869,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5868, 116, 5862, 4978, 173, 5860])).
% 1.54/1.73 tff(5870,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[226, 5869])).
% 1.54/1.73 tff(5871,plain,
% 1.54/1.73 (~r(z, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1572, 5870, 5857])).
% 1.54/1.73 tff(5872,plain,
% 1.54/1.73 (b(z, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1576, 21, 5871, 1563])).
% 1.54/1.73 tff(5873,plain,
% 1.54/1.73 (~b(s(s(s(s(s(z))))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4883, 5872, 2247, 5769, 3953])).
% 1.54/1.73 tff(5874,plain,
% 1.54/1.73 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3975, 5839, 3953])).
% 1.54/1.73 tff(5875,plain,
% 1.54/1.73 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[325, 5874])).
% 1.54/1.73 tff(5876,plain,
% 1.54/1.73 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5841])).
% 1.54/1.73 tff(5877,plain,
% 1.54/1.73 (b(z, s(s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5764, 5876])).
% 1.54/1.73 tff(5878,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5879,plain,
% 1.54/1.73 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5880,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5879])).
% 1.54/1.73 tff(5881,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5880, 5878])).
% 1.54/1.73 tff(5882,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5883,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5882, 5881])).
% 1.54/1.73 tff(5884,plain,
% 1.54/1.73 (~b(z, s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5883, 116, 5877, 5769, 5872, 5875])).
% 1.54/1.73 tff(5885,plain,
% 1.54/1.73 (r(z, s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[289, 5884])).
% 1.54/1.73 tff(5886,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.54/1.73 tff(5887,plain,
% 1.54/1.73 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 5886])).
% 1.54/1.73 tff(5888,plain,
% 1.54/1.73 (r(s(s(s(s(s(z))))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[898, 21, 895, 4867])).
% 1.54/1.73 tff(5889,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5890,plain,
% 1.54/1.73 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5891,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5890])).
% 1.54/1.73 tff(5892,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5891, 5889])).
% 1.54/1.73 tff(5893,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5894,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5893, 5892])).
% 1.54/1.73 tff(5895,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5894, 77, 293, 1212, 5888, 5887])).
% 1.54/1.73 tff(5896,plain,(b(s(s(s(s(s(z))))), s(s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | b(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(5897,plain,
% 1.54/1.73 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5896, 5885, 5857, 5873])).
% 1.54/1.73 tff(5898,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5899,plain,
% 1.54/1.73 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5900,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5899])).
% 1.54/1.73 tff(5901,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5900, 5898])).
% 1.54/1.73 tff(5902,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5903,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5902, 5901])).
% 1.54/1.73 tff(5904,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5903, 77, 229, 3953, 65])).
% 1.54/1.73 tff(5905,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(5906,plain,
% 1.54/1.73 (~r(s(s(s(z))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5905, 5870, 3953])).
% 1.54/1.73 tff(5907,plain,
% 1.54/1.73 (b(s(s(s(z))), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[89, 21, 5906, 56])).
% 1.54/1.73 tff(5908,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5909,plain,
% 1.54/1.73 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5910,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5909])).
% 1.54/1.73 tff(5911,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5910, 5908])).
% 1.54/1.73 tff(5912,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5913,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5912, 5911])).
% 1.54/1.73 tff(5914,plain,
% 1.54/1.73 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5913, 116, 2247, 5862, 5907, 5897])).
% 1.54/1.73 tff(5915,plain,
% 1.54/1.73 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5914, 5849])).
% 1.54/1.73 tff(5916,plain,
% 1.54/1.73 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5841])).
% 1.54/1.73 tff(5917,plain,
% 1.54/1.73 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(elem!1)) = elem!1)),
% 1.54/1.73 inference(symmetry,[status(thm)],[5916])).
% 1.54/1.73 tff(5918,plain,
% 1.54/1.73 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.54/1.73 inference(symmetry,[status(thm)],[5845])).
% 1.54/1.73 tff(5919,plain,
% 1.54/1.73 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5918])).
% 1.54/1.73 tff(5920,plain,
% 1.54/1.73 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = elem!1)),
% 1.54/1.73 inference(transitivity,[status(thm)],[5919, 5917])).
% 1.54/1.73 tff(5921,plain,
% 1.54/1.73 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5920])).
% 1.54/1.73 tff(5922,plain,
% 1.54/1.73 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[1138, 5921])).
% 1.54/1.73 tff(5923,plain,
% 1.54/1.73 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5845])).
% 1.54/1.73 tff(5924,plain,
% 1.54/1.73 (b(s(s(s(s(s(z))))), z) <=> b(s(s(elem!1)), z)),
% 1.54/1.73 inference(symmetry,[status(thm)],[5923])).
% 1.54/1.73 tff(5925,plain,
% 1.54/1.73 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(elem!1)), z))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5924])).
% 1.54/1.73 tff(5926,plain,
% 1.54/1.73 (~b(s(s(elem!1)), z)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5873, 5925])).
% 1.54/1.73 tff(5927,plain,
% 1.54/1.73 (r(s(s(elem!1)), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3219, 5926])).
% 1.54/1.73 tff(5928,plain,
% 1.54/1.73 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5269, 446])).
% 1.54/1.73 tff(5929,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5930,plain,
% 1.54/1.73 (((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5931,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5930])).
% 1.54/1.73 tff(5932,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5931, 5929])).
% 1.54/1.73 tff(5933,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5934,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5933, 5932])).
% 1.54/1.73 tff(5935,plain,
% 1.54/1.73 (~r(s(s(z)), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5934, 77, 752, 66, 3208])).
% 1.54/1.73 tff(5936,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 1.54/1.73 tff(5937,plain,
% 1.54/1.73 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5938,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5939,plain,
% 1.54/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5938, 5937])).
% 1.54/1.73 tff(5940,plain,
% 1.54/1.73 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5939, 21, 5936, 5935])).
% 1.54/1.73 tff(5941,plain,
% 1.54/1.73 (~r(s(z), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[162, 77, 155, 66])).
% 1.54/1.73 tff(5942,plain,
% 1.54/1.73 (b(s(z), s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[170, 21, 54, 5941])).
% 1.54/1.73 tff(5943,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5944,plain,
% 1.54/1.73 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5945,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5944])).
% 1.54/1.73 tff(5946,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5945, 5943])).
% 1.54/1.73 tff(5947,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5948,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5947, 5946])).
% 1.54/1.73 tff(5949,plain,
% 1.54/1.73 (~r(s(z), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5948, 77, 155, 3208])).
% 1.54/1.73 tff(5950,plain,
% 1.54/1.73 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[716, 21, 5949])).
% 1.54/1.73 tff(5951,plain,
% 1.54/1.73 (b(s(z), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5950, 706])).
% 1.54/1.73 tff(5952,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5953,plain,
% 1.54/1.73 (((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(5954,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[5953])).
% 1.54/1.73 tff(5955,plain,
% 1.54/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[5954, 5952])).
% 1.54/1.73 tff(5956,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(5957,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[5956, 5955])).
% 1.54/1.73 tff(5958,plain,
% 1.54/1.73 (~r(s(s(elem!1)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[5957, 77, 155, 3208])).
% 1.54/1.73 tff(5959,plain,
% 1.54/1.73 (b(s(s(elem!1)), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[808, 5958])).
% 1.54/1.73 tff(5960,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(5961,plain,
% 1.54/1.74 (((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(5962,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[5961])).
% 1.54/1.74 tff(5963,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[5962, 5960])).
% 1.54/1.74 tff(5964,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(5965,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[5964, 5963])).
% 1.54/1.74 tff(5966,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5965, 116, 5959, 5951, 5942, 5940])).
% 1.54/1.74 tff(5967,plain,((~r(s(s(z)), z)) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(5968,plain,
% 1.54/1.74 (~r(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5967, 5928, 752, 3208, 155])).
% 1.54/1.74 tff(5969,plain,
% 1.54/1.74 (b(s(s(z)), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[25, 5968])).
% 1.54/1.74 tff(5970,plain,
% 1.54/1.74 (~r(elem!1, z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3216, 752, 3208])).
% 1.54/1.74 tff(5971,plain,
% 1.54/1.74 (b(elem!1, z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[545, 439, 5970])).
% 1.54/1.74 tff(5972,plain,
% 1.54/1.74 (~b(s(s(z)), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2658, 116, 1053, 5971, 5969])).
% 1.54/1.74 tff(5973,plain,
% 1.54/1.74 (r(s(s(z)), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[426, 5972, 422])).
% 1.54/1.74 tff(5974,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(5975,plain,
% 1.54/1.74 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(5976,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[5975])).
% 1.54/1.74 tff(5977,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[5976, 5974])).
% 1.54/1.74 tff(5978,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(5979,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 1.54/1.74 tff(5980,plain,
% 1.54/1.74 (~r(s(s(z)), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5979, 77, 752, 5973])).
% 1.54/1.74 tff(5981,plain,
% 1.54/1.74 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5939, 21, 5928, 5980])).
% 1.54/1.74 tff(5982,plain,
% 1.54/1.74 (~r(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4006, 77, 360, 5973])).
% 1.54/1.74 tff(5983,plain,
% 1.54/1.74 (b(s(z), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[170, 21, 54, 5982])).
% 1.54/1.74 tff(5984,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5965, 116, 5959, 5951, 5983, 5981])).
% 1.54/1.74 tff(5985,plain,((elem!1 = z) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(5986,plain,
% 1.54/1.74 (~r(s(s(elem!1)), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5985, 5927, 439, 422, 155, 5767, 1052])).
% 1.54/1.74 tff(5987,plain,
% 1.54/1.74 (b(s(s(elem!1)), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[743, 5986, 5922])).
% 1.54/1.74 tff(5988,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5987, 5915])).
% 1.54/1.74 tff(5989,plain,((~r(s(z), z)) | (elem!1 = z) | (s(s(z)) = elem!1) | r(z, elem!1) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | b(s(z), elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(5990,plain,
% 1.54/1.74 (~r(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5989, 1052, 422, 439, 2247, 3953, 1331, 66, 340, 537])).
% 1.54/1.74 tff(5991,plain,
% 1.54/1.74 (b(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[210, 5990])).
% 1.54/1.74 tff(5992,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(5993,plain,
% 1.54/1.74 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(5994,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[5993])).
% 1.54/1.74 tff(5995,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[5994, 5992])).
% 1.54/1.74 tff(5996,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(5997,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[5996, 5995])).
% 1.54/1.74 tff(5998,plain,
% 1.54/1.74 (~b(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5997, 116, 5764, 537, 5991, 2247])).
% 1.54/1.74 tff(5999,plain,
% 1.54/1.74 (r(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[194, 5998])).
% 1.54/1.74 tff(6000,plain,
% 1.54/1.74 (~r(elem!1, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[368, 5999, 5767])).
% 1.54/1.74 tff(6001,plain,
% 1.54/1.74 (elem!1 = s(s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1345, 6000, 5765])).
% 1.54/1.74 tff(6002,plain,
% 1.54/1.74 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6001])).
% 1.54/1.74 tff(6003,plain,
% 1.54/1.74 (b(z, s(s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[5764, 6002])).
% 1.54/1.74 tff(6004,plain,
% 1.54/1.74 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6001])).
% 1.54/1.74 tff(6005,plain,
% 1.54/1.74 (b(s(s(z)), s(s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[1331, 6004])).
% 1.54/1.74 tff(6006,plain,
% 1.54/1.74 (s(elem!1) = s(s(s(s(z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6001])).
% 1.54/1.74 tff(6007,plain,
% 1.54/1.74 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6006])).
% 1.54/1.74 tff(6008,plain,
% 1.54/1.74 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6007, 1393])).
% 1.54/1.74 tff(6009,plain,
% 1.54/1.74 ((~(s(elem!1) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6008])).
% 1.54/1.74 tff(6010,plain,
% 1.54/1.74 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3975, 5999, 3953])).
% 1.54/1.74 tff(6011,plain,
% 1.54/1.74 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[325, 6010])).
% 1.54/1.74 tff(6012,plain,
% 1.54/1.74 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4700, 6011, 340])).
% 1.54/1.74 tff(6013,plain,
% 1.54/1.74 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1364, 6012])).
% 1.54/1.74 tff(6014,plain,
% 1.54/1.74 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6013, 6009])).
% 1.54/1.74 tff(6015,plain,
% 1.54/1.74 (~b(s(s(s(s(z)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4732, 6011, 537, 5764, 5991])).
% 1.54/1.74 tff(6016,plain,
% 1.54/1.74 (r(s(s(s(s(z)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[247, 6015])).
% 1.54/1.74 tff(6017,plain,
% 1.54/1.74 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[237, 6016, 66])).
% 1.54/1.74 tff(6018,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[226, 6017])).
% 1.54/1.74 tff(6019,plain,
% 1.54/1.74 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3975, 292, 3953])).
% 1.54/1.74 tff(6020,plain,
% 1.54/1.74 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[325, 6019])).
% 1.54/1.74 tff(6021,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.74 tff(6022,plain,
% 1.54/1.74 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4709, 77, 3953, 1904])).
% 1.54/1.74 tff(6023,plain,
% 1.54/1.74 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1405, 6022, 6021])).
% 1.54/1.74 tff(6024,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6025,plain,
% 1.54/1.74 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6026,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6025])).
% 1.54/1.74 tff(6027,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6026, 6024])).
% 1.54/1.74 tff(6028,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6029,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6028, 6027])).
% 1.54/1.74 tff(6030,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6029, 116, 212, 27, 6023, 6020, 2311])).
% 1.54/1.74 tff(6031,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6032,plain,
% 1.54/1.74 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6031, 6018, 6005, 6014, 3953, 5999])).
% 1.54/1.74 tff(6033,plain,
% 1.54/1.74 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1380, 6032])).
% 1.54/1.74 tff(6034,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6035,plain,
% 1.54/1.74 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6036,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6035])).
% 1.54/1.74 tff(6037,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6036, 6034])).
% 1.54/1.74 tff(6038,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6039,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6038, 6037])).
% 1.54/1.74 tff(6040,plain,
% 1.54/1.74 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6039, 116, 271, 2247, 27, 5031])).
% 1.54/1.74 tff(6041,plain,
% 1.54/1.74 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 6040])).
% 1.54/1.74 tff(6042,plain,
% 1.54/1.74 (~b(s(s(s(s(s(z))))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2383, 116, 271, 2247, 255, 5031])).
% 1.54/1.74 tff(6043,plain,
% 1.54/1.74 (r(s(s(s(s(s(z))))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[898, 21, 895, 6042])).
% 1.54/1.74 tff(6044,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6045,plain,
% 1.54/1.74 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6046,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6045])).
% 1.54/1.74 tff(6047,plain,
% 1.54/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6046, 6044])).
% 1.54/1.74 tff(6048,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(6049,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[6048, 6047])).
% 1.54/1.74 tff(6050,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6049, 77, 1212, 6043, 6041])).
% 1.54/1.74 tff(6051,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(6052,plain,
% 1.54/1.74 (~b(z, s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[6051, 6033, 5857, 2247, 6005, 6003])).
% 1.54/1.74 tff(6053,plain,
% 1.54/1.74 (r(z, s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[289, 6052])).
% 1.54/1.74 tff(6054,plain,
% 1.54/1.74 (~b(s(s(s(s(s(z))))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[5120, 116, 2247, 6003, 6033])).
% 1.54/1.74 tff(6055,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6056,plain,
% 1.54/1.74 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(6057,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[6056])).
% 1.54/1.74 tff(6058,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[6057, 6055])).
% 1.54/1.74 tff(6059,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6060,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6059, 6058])).
% 1.54/1.75 tff(6061,plain,
% 1.54/1.75 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6060, 116, 2247, 6003, 6005, 6033])).
% 1.54/1.75 tff(6062,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[5896, 6061, 6054, 5857, 6053])).
% 1.54/1.75 tff(6063,plain,(r(z, elem!1) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~b(elem!1, z)) | b(s(z), elem!1) | (s(s(z)) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6064,plain,
% 1.54/1.75 (r(z, elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6063, 4804, 3952, 5629, 26, 5455, 340, 5628, 5626])).
% 1.54/1.75 tff(6065,plain,
% 1.54/1.75 (~r(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[690, 6064, 5763])).
% 1.54/1.75 tff(6066,plain,
% 1.54/1.75 (b(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[210, 6065])).
% 1.54/1.75 tff(6067,plain,
% 1.54/1.75 (~r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3295, 6064, 5763])).
% 1.54/1.75 tff(6068,plain,
% 1.54/1.75 (b(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[289, 6067])).
% 1.54/1.75 tff(6069,plain,
% 1.54/1.75 (~b(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3291, 6068, 4804, 6066])).
% 1.54/1.75 tff(6070,plain,
% 1.54/1.75 (r(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[194, 6069])).
% 1.54/1.75 tff(6071,plain,
% 1.54/1.75 (~r(elem!1, s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[368, 6070, 5763])).
% 1.54/1.75 tff(6072,plain,
% 1.54/1.75 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4113, 6071, 3946])).
% 1.54/1.75 tff(6073,plain,
% 1.54/1.75 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3975, 6070, 3952])).
% 1.54/1.75 tff(6074,plain,
% 1.54/1.75 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[325, 6073])).
% 1.54/1.75 tff(6075,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[279, 6074, 6066, 6068])).
% 1.54/1.75 tff(6076,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[247, 6075])).
% 1.54/1.75 tff(6077,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3287, 6076, 6064])).
% 1.54/1.75 tff(6078,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1596, 6077, 6072])).
% 1.54/1.75 tff(6079,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[237, 6076, 26])).
% 1.54/1.75 tff(6080,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[226, 6079])).
% 1.54/1.75 tff(6081,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6082,plain,
% 1.54/1.75 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6083,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6082])).
% 1.54/1.75 tff(6084,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6083, 6081])).
% 1.54/1.75 tff(6085,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6086,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6085, 6084])).
% 1.54/1.75 tff(6087,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6086, 116, 5455, 6068, 6080, 5629, 6078])).
% 1.54/1.75 tff(6088,plain,(b(s(z), elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6089,plain,
% 1.54/1.75 (b(s(z), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6088, 2])).
% 1.54/1.75 tff(6090,plain,
% 1.54/1.75 (r(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[194, 1664])).
% 1.54/1.75 tff(6091,plain,
% 1.54/1.75 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3975, 6090, 3987])).
% 1.54/1.75 tff(6092,plain,
% 1.54/1.75 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[325, 6091])).
% 1.54/1.75 tff(6093,plain,
% 1.54/1.75 (~b(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[279, 6092, 270, 447])).
% 1.54/1.75 tff(6094,plain,
% 1.54/1.75 (r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[289, 6093])).
% 1.54/1.75 tff(6095,plain,
% 1.54/1.75 (~b(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2085, 2040, 847, 270])).
% 1.54/1.75 tff(6096,plain,
% 1.54/1.75 (r(elem!1, z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2115, 518, 847, 1052, 270])).
% 1.54/1.75 tff(6097,plain,
% 1.54/1.75 (~r(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2095, 6096, 293])).
% 1.54/1.75 tff(6098,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[633, 6097, 6095, 3670])).
% 1.54/1.75 tff(6099,plain,((z = elem!1) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6100,plain,
% 1.54/1.75 (z = elem!1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6099, 6094, 847, 270, 1052])).
% 1.54/1.75 tff(6101,plain,
% 1.54/1.75 (s(z) = s(elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6100])).
% 1.54/1.75 tff(6102,plain,
% 1.54/1.75 (s(s(z)) = s(s(elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6101])).
% 1.54/1.75 tff(6103,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6102])).
% 1.54/1.75 tff(6104,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[176, 6103])).
% 1.54/1.75 tff(6105,plain,
% 1.54/1.75 (elem!1 = z),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[445, 6100])).
% 1.54/1.75 tff(6106,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2421, 6105, 240])).
% 1.54/1.75 tff(6107,plain,
% 1.54/1.75 (~r(z, s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[301, 6094, 6090])).
% 1.54/1.75 tff(6108,plain,
% 1.54/1.75 (~r(elem!1, s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2488, 6105, 6107])).
% 1.54/1.75 tff(6109,plain,
% 1.54/1.75 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4113, 6108, 3986])).
% 1.54/1.75 tff(6110,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1596, 6109, 6106])).
% 1.54/1.75 tff(6111,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6101])).
% 1.54/1.75 tff(6112,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4668, 77, 3987, 6090])).
% 1.54/1.75 tff(6113,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2054, 21, 6112])).
% 1.54/1.75 tff(6114,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6113, 2044])).
% 1.54/1.75 tff(6115,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6114, 6111])).
% 1.54/1.75 tff(6116,plain,
% 1.54/1.75 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1709])).
% 1.54/1.75 tff(6117,plain,
% 1.54/1.75 (b(s(elem!1), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[847, 6116])).
% 1.54/1.75 tff(6118,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[779, 6117])).
% 1.54/1.75 tff(6119,plain,((~b(s(z), elem!1)) | b(s(elem!1), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6120,plain,
% 1.54/1.75 (b(s(elem!1), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6119, 6100, 847])).
% 1.54/1.75 tff(6121,plain,
% 1.54/1.75 (~(elem!1 = s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1667, 1664, 847])).
% 1.54/1.75 tff(6122,plain,
% 1.54/1.75 (b(elem!1, s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1345, 6108, 6121])).
% 1.54/1.75 tff(6123,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6124,plain,
% 1.54/1.75 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6125,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6124])).
% 1.54/1.75 tff(6126,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6125, 6123])).
% 1.54/1.75 tff(6127,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6128,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6127, 6126])).
% 1.54/1.75 tff(6129,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6128, 116, 6122, 6120, 6115, 6110, 6104])).
% 1.54/1.75 tff(6130,plain,(b(s(z), s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), z) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6131,plain,
% 1.54/1.75 (b(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6130, 1052, 3946, 3962, 6089, 3965, 3985])).
% 1.54/1.75 tff(6132,plain,
% 1.54/1.75 (~b(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[184, 6131, 3983, 3985])).
% 1.54/1.75 tff(6133,plain,
% 1.54/1.75 (~(s(s(z)) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2038, 6132, 6089])).
% 1.54/1.75 tff(6134,plain,
% 1.54/1.75 (r(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[172, 6132])).
% 1.54/1.75 tff(6135,plain,
% 1.54/1.75 (~b(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4427, 116, 3983, 3985, 6131])).
% 1.54/1.75 tff(6136,plain,
% 1.54/1.75 (r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[391, 21, 6135, 388])).
% 1.54/1.75 tff(6137,plain,
% 1.54/1.75 (~r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3659, 6136, 26])).
% 1.54/1.75 tff(6138,plain,
% 1.54/1.75 (b(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[289, 6137])).
% 1.54/1.75 tff(6139,plain,
% 1.54/1.75 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[279, 6138, 3965, 3963])).
% 1.54/1.75 tff(6140,plain,
% 1.54/1.75 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[325, 6139])).
% 1.54/1.75 tff(6141,plain,
% 1.54/1.75 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[336, 6140, 6134])).
% 1.54/1.75 tff(6142,plain,
% 1.54/1.75 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[149, 6141])).
% 1.54/1.75 tff(6143,plain,
% 1.54/1.75 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3873, 6139, 6089])).
% 1.54/1.75 tff(6144,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6145,plain,
% 1.54/1.75 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6146,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6145])).
% 1.54/1.75 tff(6147,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6146, 6144])).
% 1.54/1.75 tff(6148,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6149,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6148, 6147])).
% 1.54/1.75 tff(6150,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6149, 116, 6089, 3965, 6138, 3963])).
% 1.54/1.75 tff(6151,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2054, 21, 6150])).
% 1.54/1.75 tff(6152,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6151, 2044])).
% 1.54/1.75 tff(6153,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.75 tff(6154,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1319, 77, 575, 66, 428])).
% 1.54/1.75 tff(6155,plain,((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6156,plain,
% 1.54/1.75 (~r(s(s(z)), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6155, 6096, 66])).
% 1.54/1.75 tff(6157,plain,
% 1.54/1.75 (b(s(s(z)), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[426, 6156, 422])).
% 1.54/1.75 tff(6158,plain,
% 1.54/1.75 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2661, 6157, 2410, 534, 2040, 2416])).
% 1.54/1.75 tff(6159,plain,
% 1.54/1.75 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1068, 6158, 1362])).
% 1.54/1.75 tff(6160,plain,
% 1.54/1.75 (r(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[633, 6095, 3670])).
% 1.54/1.75 tff(6161,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6162,plain,
% 1.54/1.75 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6163,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6162])).
% 1.54/1.75 tff(6164,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6163, 6161])).
% 1.54/1.75 tff(6165,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6166,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6165, 6164])).
% 1.54/1.75 tff(6167,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6166, 77, 6160, 6159, 3953, 6153])).
% 1.54/1.75 tff(6168,plain,((z = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6169,plain,
% 1.54/1.75 (z = elem!1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6168, 6152, 3952, 6143, 6142, 6133, 26, 6089, 3965, 1052])).
% 1.54/1.75 tff(6170,plain,
% 1.54/1.75 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6169])).
% 1.54/1.75 tff(6171,plain,
% 1.54/1.75 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.54/1.75 inference(symmetry,[status(thm)],[6170])).
% 1.54/1.75 tff(6172,plain,
% 1.54/1.75 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6171])).
% 1.54/1.75 tff(6173,plain,
% 1.54/1.75 (~b(elem!1, z)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3544, 6172])).
% 1.54/1.75 tff(6174,plain,
% 1.54/1.75 (elem!1 = z),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[445, 6169])).
% 1.54/1.75 tff(6175,plain,
% 1.54/1.75 (~b(s(s(z)), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1680, 6174, 2])).
% 1.54/1.75 tff(6176,plain,
% 1.54/1.75 (~b(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[184, 175, 152, 154])).
% 1.54/1.75 tff(6177,plain,
% 1.54/1.75 (~(s(s(z)) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2038, 6176, 847])).
% 1.54/1.75 tff(6178,plain,
% 1.54/1.75 (r(s(s(z)), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[426, 6177, 1])).
% 1.54/1.75 tff(6179,plain,
% 1.54/1.75 (~r(elem!1, z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6155, 6178, 66])).
% 1.54/1.75 tff(6180,plain,
% 1.54/1.75 (z = elem!1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2115, 6179, 847, 1052, 3989])).
% 1.54/1.75 tff(6181,plain,
% 1.54/1.75 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6180])).
% 1.54/1.75 tff(6182,plain,
% 1.54/1.75 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6181])).
% 1.54/1.75 tff(6183,plain,
% 1.54/1.75 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[895, 6182])).
% 1.54/1.75 tff(6184,plain,
% 1.54/1.75 (s(z) = s(elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6180])).
% 1.54/1.75 tff(6185,plain,
% 1.54/1.75 (s(s(z)) = s(s(elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6184])).
% 1.54/1.75 tff(6186,plain,
% 1.54/1.75 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6185])).
% 1.54/1.75 tff(6187,plain,
% 1.54/1.75 (r(s(s(elem!1)), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6178, 6186])).
% 1.54/1.75 tff(6188,plain,
% 1.54/1.75 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6180])).
% 1.54/1.75 tff(6189,plain,
% 1.54/1.75 (r(s(s(s(z))), elem!1)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[67, 6188])).
% 1.54/1.75 tff(6190,plain,
% 1.54/1.75 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6185])).
% 1.54/1.75 tff(6191,plain,
% 1.54/1.75 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6190, 1504])).
% 1.54/1.75 tff(6192,plain,
% 1.54/1.75 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6191])).
% 1.54/1.75 tff(6193,plain,
% 1.54/1.75 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[1202, 6192])).
% 1.54/1.75 tff(6194,plain,
% 1.54/1.75 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6185])).
% 1.54/1.75 tff(6195,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[152, 6194])).
% 1.54/1.75 tff(6196,plain,
% 1.54/1.75 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1782, 6180])).
% 1.54/1.75 tff(6197,plain,
% 1.54/1.75 (s(elem!1) = s(z)),
% 1.54/1.75 inference(symmetry,[status(thm)],[6184])).
% 1.54/1.75 tff(6198,plain,
% 1.54/1.75 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6197])).
% 1.54/1.75 tff(6199,plain,
% 1.54/1.75 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6198])).
% 1.54/1.75 tff(6200,plain,
% 1.54/1.75 (~b(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4427, 116, 152, 154, 175])).
% 1.54/1.75 tff(6201,plain,
% 1.54/1.75 (r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[391, 21, 6200, 388])).
% 1.54/1.75 tff(6202,plain,
% 1.54/1.75 (~r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3659, 6201, 66])).
% 1.54/1.75 tff(6203,plain,
% 1.54/1.75 (b(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[289, 6202])).
% 1.54/1.75 tff(6204,plain,
% 1.54/1.75 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[279, 6203, 3989, 447])).
% 1.54/1.75 tff(6205,plain,
% 1.54/1.75 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[325, 6204])).
% 1.54/1.75 tff(6206,plain,
% 1.54/1.75 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6205, 6199])).
% 1.54/1.75 tff(6207,plain,
% 1.54/1.75 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6184, 6185])).
% 1.54/1.75 tff(6208,plain,
% 1.54/1.75 (r(s(z), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[172, 6176])).
% 1.54/1.75 tff(6209,plain,
% 1.54/1.75 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6208, 6207])).
% 1.54/1.75 tff(6210,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6185])).
% 1.54/1.75 tff(6211,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[154, 6210])).
% 1.54/1.75 tff(6212,plain,
% 1.54/1.75 (elem!1 = z),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[545, 6179, 1455])).
% 1.54/1.75 tff(6213,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6185])).
% 1.54/1.75 tff(6214,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6213])).
% 1.54/1.75 tff(6215,plain,
% 1.54/1.75 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6214])).
% 1.54/1.75 tff(6216,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6197])).
% 1.54/1.75 tff(6217,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6216, 1752])).
% 1.54/1.75 tff(6218,plain,
% 1.54/1.75 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6217])).
% 1.54/1.75 tff(6219,plain,
% 1.54/1.75 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6218])).
% 1.54/1.75 tff(6220,plain,
% 1.54/1.75 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[320, 6219])).
% 1.54/1.75 tff(6221,plain,
% 1.54/1.75 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3873, 6204, 847])).
% 1.54/1.75 tff(6222,plain,
% 1.54/1.75 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1584, 6221])).
% 1.54/1.75 tff(6223,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2421, 6212, 240])).
% 1.54/1.75 tff(6224,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1596, 6223, 6222])).
% 1.54/1.75 tff(6225,plain,
% 1.54/1.75 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[442])).
% 1.54/1.75 tff(6226,plain,
% 1.54/1.75 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6225])).
% 1.54/1.75 tff(6227,plain,
% 1.54/1.75 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6226])).
% 1.54/1.75 tff(6228,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.54/1.75 tff(6229,plain,
% 1.54/1.75 (~b(z, s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6228, 6227])).
% 1.54/1.75 tff(6230,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[271, 6229])).
% 1.54/1.75 tff(6231,plain,((~(z = elem!1)) | (~b(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6232,plain,
% 1.54/1.75 (b(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6231, 6180, 6203])).
% 1.54/1.75 tff(6233,plain,
% 1.54/1.75 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1710])).
% 1.54/1.75 tff(6234,plain,
% 1.54/1.75 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[6233])).
% 1.54/1.75 tff(6235,plain,
% 1.54/1.75 (b(elem!1, s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[667, 6234])).
% 1.54/1.75 tff(6236,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.54/1.75 tff(6237,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6236, 6235])).
% 1.54/1.75 tff(6238,plain,((~b(elem!1, s(z))) | b(elem!1, s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(6239,plain,
% 1.54/1.75 (b(elem!1, s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6238, 6232, 6180])).
% 1.54/1.75 tff(6240,plain,
% 1.54/1.75 (b(s(elem!1), elem!1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6119, 6180, 847])).
% 1.54/1.75 tff(6241,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6242,plain,
% 1.54/1.75 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6243,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6242])).
% 1.54/1.75 tff(6244,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[6243, 6241])).
% 1.54/1.75 tff(6245,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(6246,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6245, 6244])).
% 1.54/1.75 tff(6247,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6246, 116, 6240, 6239, 6224])).
% 1.54/1.75 tff(6248,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1776, 21, 6247])).
% 1.54/1.75 tff(6249,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[6248, 6220])).
% 1.54/1.75 tff(6250,plain,
% 1.54/1.75 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[6185, 6184])).
% 1.54/1.75 tff(6251,plain,
% 1.54/1.75 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[6201, 6250])).
% 1.54/1.75 tff(6252,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(6253,plain,
% 1.54/1.75 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6254,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6253])).
% 1.54/1.76 tff(6255,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6254, 6252])).
% 1.54/1.76 tff(6256,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6257,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6256, 6255])).
% 1.54/1.76 tff(6258,plain,
% 1.54/1.76 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6257, 77, 6187, 6251, 6249])).
% 1.54/1.76 tff(6259,plain,
% 1.54/1.76 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6258, 6215])).
% 1.54/1.76 tff(6260,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[226, 6259])).
% 1.54/1.76 tff(6261,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3559, 6260, 6212])).
% 1.54/1.76 tff(6262,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6263,plain,
% 1.54/1.76 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6264,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6263])).
% 1.54/1.76 tff(6265,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6264, 6262])).
% 1.54/1.76 tff(6266,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6267,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6266, 6265])).
% 1.54/1.76 tff(6268,plain,
% 1.54/1.76 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6267, 116, 6261, 6211, 6195])).
% 1.54/1.76 tff(6269,plain,
% 1.54/1.76 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1146, 6268])).
% 1.54/1.76 tff(6270,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6271,plain,
% 1.54/1.76 (((~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(elem!1)))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6272,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6271])).
% 1.54/1.76 tff(6273,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6272, 6270])).
% 1.54/1.76 tff(6274,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6275,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6274, 6273])).
% 1.54/1.76 tff(6276,plain,
% 1.54/1.76 (~r(s(s(s(z))), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6275, 77, 6269, 6209, 6206])).
% 1.54/1.76 tff(6277,plain,
% 1.54/1.76 (b(s(s(s(z))), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1853, 6276, 6196])).
% 1.54/1.76 tff(6278,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6279,plain,
% 1.54/1.76 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6280,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6279])).
% 1.54/1.76 tff(6281,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6280, 6278])).
% 1.54/1.76 tff(6282,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6283,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6282, 6281])).
% 1.54/1.76 tff(6284,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)],[6283, 77, 638, 1027])).
% 1.54/1.76 tff(6285,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)],[1380, 6284])).
% 1.54/1.76 tff(6286,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.54/1.76 tff(6287,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6288,plain,
% 1.54/1.76 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6289,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6288])).
% 1.54/1.76 tff(6290,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6289, 6287])).
% 1.54/1.76 tff(6291,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6292,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6291, 6290])).
% 1.54/1.76 tff(6293,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6292, 116, 846, 6286, 6285, 3562, 1029])).
% 1.54/1.76 tff(6294,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(6295,plain,
% 1.54/1.76 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6294, 6240, 6277, 6195, 6193, 6189, 6187])).
% 1.54/1.76 tff(6296,plain,
% 1.54/1.76 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[885, 6295, 6183])).
% 1.54/1.76 tff(6297,plain,
% 1.54/1.76 (~(s(s(s(z))) = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1749, 6180])).
% 1.54/1.76 tff(6298,plain,
% 1.54/1.76 (~(elem!1 = s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6297, 1744])).
% 1.54/1.76 tff(6299,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6300,plain,
% 1.54/1.76 (((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6301,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6300])).
% 1.54/1.76 tff(6302,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6301, 6299])).
% 1.54/1.76 tff(6303,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6304,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6303, 6302])).
% 1.54/1.76 tff(6305,plain,
% 1.54/1.76 (~b(elem!1, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[6304, 116, 6240, 6239, 6277])).
% 1.54/1.76 tff(6306,plain,
% 1.54/1.76 (r(elem!1, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1345, 6305, 6298])).
% 1.54/1.76 tff(6307,plain,
% 1.54/1.76 (r(z, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2488, 6306, 6212])).
% 1.54/1.76 tff(6308,plain,
% 1.54/1.76 (~r(z, s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2461, 6307, 6269])).
% 1.54/1.76 tff(6309,plain,
% 1.54/1.76 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2440, 6308, 6212])).
% 1.54/1.76 tff(6310,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1068, 6309, 6221])).
% 1.54/1.76 tff(6311,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6312,plain,
% 1.54/1.76 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, 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)))))))) <=> ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6313,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[6312])).
% 1.54/1.76 tff(6314,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[6313, 6311])).
% 1.54/1.76 tff(6315,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, 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))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(6316,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[6315, 6314])).
% 1.54/1.76 tff(6317,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)],[6316, 116, 6310, 6261, 6224, 6296])).
% 1.54/1.76 tff(6318,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)],[1940, 21, 6317, 1708])).
% 1.54/1.76 tff(6319,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(6320,plain,
% 1.54/1.76 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6321,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6320])).
% 1.54/1.77 tff(6322,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[6321, 6319])).
% 1.54/1.77 tff(6323,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(6324,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6323, 6322])).
% 1.54/1.77 tff(6325,plain,
% 1.54/1.77 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6324, 116, 6310, 6240, 6261, 6296])).
% 1.54/1.77 tff(6326,plain,
% 1.54/1.77 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1364, 6221])).
% 1.54/1.77 tff(6327,plain,
% 1.54/1.77 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[858, 21, 6326, 6325])).
% 1.54/1.77 tff(6328,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[5381, 77, 6249, 6327, 6318])).
% 1.54/1.77 tff(6329,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | r(s(s(s(s(z)))), z) | (~b(s(z), elem!1)) | b(elem!1, z) | r(z, elem!1) | (~r(s(s(z)), z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6330,plain,
% 1.54/1.77 (b(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6329, 6175, 3962, 6089, 6131, 1052, 26, 67])).
% 1.54/1.77 tff(6331,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6330, 6173])).
% 1.54/1.77 tff(6332,plain,(r(z, elem!1) | (~r(s(s(s(z))), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6333,plain,
% 1.54/1.77 (r(z, elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6332, 67, 2])).
% 1.54/1.77 tff(6334,plain,
% 1.54/1.77 (s(elem!1) = s(s(s(z)))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3674])).
% 1.54/1.77 tff(6335,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)],[6334])).
% 1.54/1.77 tff(6336,plain,
% 1.54/1.77 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 1.54/1.77 inference(symmetry,[status(thm)],[6335])).
% 1.54/1.77 tff(6337,plain,
% 1.54/1.77 (b(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2038, 3672, 6089])).
% 1.54/1.77 tff(6338,plain,
% 1.54/1.77 (~b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[184, 6337, 27, 176])).
% 1.54/1.77 tff(6339,plain,
% 1.54/1.77 (r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[194, 6338])).
% 1.54/1.77 tff(6340,plain,
% 1.54/1.77 (r(s(z), s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6339, 6336])).
% 1.54/1.77 tff(6341,plain,
% 1.54/1.77 (~(s(s(elem!1)) = elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[529, 3672, 1687])).
% 1.54/1.77 tff(6342,plain,
% 1.54/1.77 (~(elem!1 = s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3669, 6089])).
% 1.54/1.77 tff(6343,plain,
% 1.54/1.77 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3975, 6339, 3952])).
% 1.54/1.77 tff(6344,plain,
% 1.54/1.77 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[325, 6343])).
% 1.54/1.77 tff(6345,plain,
% 1.54/1.77 (~b(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[279, 6344, 270, 254])).
% 1.54/1.77 tff(6346,plain,
% 1.54/1.77 (r(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[289, 6345])).
% 1.54/1.77 tff(6347,plain,
% 1.54/1.77 (~r(elem!1, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[791, 6346, 448])).
% 1.54/1.77 tff(6348,plain,
% 1.54/1.77 (b(elem!1, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[633, 6347, 6342])).
% 1.54/1.77 tff(6349,plain,
% 1.54/1.77 (~(s(z) = elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1984, 6342])).
% 1.54/1.77 tff(6350,plain,
% 1.54/1.77 (b(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3705, 6346, 448, 1, 6349, 1687, 2, 254])).
% 1.54/1.77 tff(6351,plain,
% 1.54/1.77 (b(z, s(s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6350, 3676])).
% 1.54/1.77 tff(6352,plain,
% 1.54/1.77 (~b(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[540, 3672, 2])).
% 1.54/1.77 tff(6353,plain,
% 1.54/1.77 (r(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[545, 6352, 1686])).
% 1.54/1.77 tff(6354,plain,
% 1.54/1.77 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[912, 3672])).
% 1.54/1.77 tff(6355,plain,
% 1.54/1.77 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[568, 3672])).
% 1.54/1.77 tff(6356,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3675])).
% 1.54/1.77 tff(6357,plain,
% 1.54/1.77 (b(s(s(elem!1)), z)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[254, 6356])).
% 1.54/1.77 tff(6358,plain,
% 1.54/1.77 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1017, 6357, 6089, 270, 6355, 6354, 6353, 6351, 6348, 1901])).
% 1.54/1.77 tff(6359,plain,
% 1.54/1.77 (r(s(s(elem!1)), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[743, 6358, 6341])).
% 1.54/1.77 tff(6360,plain,
% 1.54/1.77 (~b(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1443, 6359, 448, 270])).
% 1.54/1.77 tff(6361,plain,
% 1.54/1.77 (r(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[808, 6360])).
% 1.54/1.77 tff(6362,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3675, 3674])).
% 1.54/1.77 tff(6363,plain,
% 1.54/1.77 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3952, 6362])).
% 1.54/1.77 tff(6364,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6365,plain,
% 1.54/1.77 (((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6366,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6365])).
% 1.54/1.77 tff(6367,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[6366, 6364])).
% 1.54/1.77 tff(6368,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(6369,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6368, 6367])).
% 1.54/1.77 tff(6370,plain,
% 1.54/1.77 ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6369, 77, 6363])).
% 1.54/1.77 tff(6371,plain,
% 1.54/1.77 (~r(s(z), s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6370, 6361])).
% 1.54/1.77 tff(6372,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6371, 6340])).
% 1.54/1.77 tff(6373,plain,(b(s(s(z)), elem!1) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | b(s(s(z)), z) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6374,plain,
% 1.54/1.77 (b(s(s(z)), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6373, 6333, 3965, 3963, 2, 3983, 3985])).
% 1.54/1.77 tff(6375,plain,
% 1.54/1.77 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[325, 313])).
% 1.54/1.77 tff(6376,plain,
% 1.54/1.77 (~r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3975, 6375, 3953])).
% 1.54/1.77 tff(6377,plain,
% 1.54/1.77 (b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[194, 6376])).
% 1.54/1.77 tff(6378,plain,
% 1.54/1.77 (~b(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[184, 6377, 27, 176])).
% 1.54/1.77 tff(6379,plain,
% 1.54/1.77 (r(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[172, 6378])).
% 1.54/1.77 tff(6380,plain,
% 1.54/1.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[336, 6379, 6375])).
% 1.54/1.77 tff(6381,plain,
% 1.54/1.77 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[149, 6380])).
% 1.54/1.77 tff(6382,plain,
% 1.54/1.77 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3873, 313, 847])).
% 1.54/1.77 tff(6383,plain,
% 1.54/1.77 (~b(elem!1, s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1340, 1331, 27, 176])).
% 1.54/1.77 tff(6384,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6385,plain,
% 1.54/1.77 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6386,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6385])).
% 1.54/1.77 tff(6387,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[6386, 6384])).
% 1.54/1.77 tff(6388,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(6389,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6388, 6387])).
% 1.54/1.77 tff(6390,plain,
% 1.54/1.77 (~b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6389, 116, 27, 176, 175, 5031])).
% 1.54/1.77 tff(6391,plain,
% 1.54/1.77 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[870, 21, 1901, 6390])).
% 1.54/1.77 tff(6392,plain,
% 1.54/1.77 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1387, 116, 27, 176, 5031])).
% 1.54/1.77 tff(6393,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 6392])).
% 1.54/1.77 tff(6394,plain,
% 1.54/1.77 (~b(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[184, 175, 27, 176])).
% 1.54/1.77 tff(6395,plain,
% 1.54/1.77 (r(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[172, 6394])).
% 1.54/1.77 tff(6396,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6397,plain,
% 1.54/1.77 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6398,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6397])).
% 1.54/1.77 tff(6399,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[6398, 6396])).
% 1.54/1.77 tff(6400,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(6401,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6400, 6399])).
% 1.54/1.77 tff(6402,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6401, 77, 6395, 6393, 6391])).
% 1.54/1.77 tff(6403,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6404,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)],[6403, 6377, 176, 27])).
% 1.54/1.77 tff(6405,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)],[1380, 6404])).
% 1.54/1.77 tff(6406,plain,
% 1.54/1.77 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1364, 6382])).
% 1.54/1.77 tff(6407,plain,
% 1.54/1.77 ((s(elem!1) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1367])).
% 1.54/1.77 tff(6408,plain,
% 1.54/1.77 ((s(elem!1) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[6407, 1752])).
% 1.54/1.77 tff(6409,plain,
% 1.54/1.77 ((s(z) = s(s(s(s(z))))) <=> (s(elem!1) = s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[6408])).
% 1.54/1.77 tff(6410,plain,
% 1.54/1.77 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6409])).
% 1.54/1.77 tff(6411,plain,
% 1.54/1.77 (~(s(elem!1) = s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[320, 6410])).
% 1.54/1.77 tff(6412,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1366])).
% 1.54/1.77 tff(6413,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[6412])).
% 1.54/1.77 tff(6414,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1904, 6413])).
% 1.54/1.77 tff(6415,plain,
% 1.54/1.77 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1367])).
% 1.54/1.77 tff(6416,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 1.54/1.77 inference(symmetry,[status(thm)],[6415])).
% 1.54/1.77 tff(6417,plain,
% 1.54/1.77 (b(s(elem!1), z)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[254, 6416])).
% 1.54/1.77 tff(6418,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3807, 6417, 6414, 1901, 448, 270, 855, 6411])).
% 1.54/1.77 tff(6419,plain,((~(elem!1 = s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6420,plain,
% 1.54/1.77 (~(elem!1 = s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6419, 6406, 270, 448, 254, 6405])).
% 1.54/1.77 tff(6421,plain,
% 1.54/1.77 (r(elem!1, s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1345, 6420, 6383])).
% 1.54/1.77 tff(6422,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4408, 77, 3953, 6421])).
% 1.54/1.77 tff(6423,plain,
% 1.54/1.77 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4401, 77, 3953, 6421])).
% 1.54/1.77 tff(6424,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4415, 6423, 6422, 1331, 6382, 6381])).
% 1.54/1.77 tff(6425,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6426,plain,
% 1.54/1.77 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6425, 6374, 3952, 3965, 6333, 3963, 3985, 3983, 6089])).
% 1.54/1.77 tff(6427,plain,
% 1.54/1.77 (~b(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[279, 6426, 3965, 3963])).
% 1.54/1.77 tff(6428,plain,
% 1.54/1.77 (r(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[289, 6427])).
% 1.54/1.77 tff(6429,plain,
% 1.54/1.77 (~r(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3659, 6428, 26])).
% 1.54/1.77 tff(6430,plain,
% 1.54/1.77 (~r(elem!1, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[791, 6428, 6333])).
% 1.54/1.77 tff(6431,plain,
% 1.54/1.77 (b(elem!1, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[633, 6430, 6342])).
% 1.54/1.77 tff(6432,plain,
% 1.54/1.77 (~b(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3714, 116, 6089, 6431, 6374])).
% 1.54/1.77 tff(6433,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[391, 21, 6432, 388, 6429])).
% 1.54/1.77 tff(6434,plain,((~r(s(s(s(z))), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6435,plain,
% 1.54/1.77 (~r(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6434, 2])).
% 1.54/1.77 tff(6436,plain,
% 1.54/1.77 (b(s(s(s(z))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[63, 6435])).
% 1.54/1.77 tff(6437,plain,
% 1.54/1.77 (~r(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[164, 3406, 66])).
% 1.54/1.77 tff(6438,plain,
% 1.54/1.77 (b(s(z), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[172, 6437])).
% 1.54/1.77 tff(6439,plain,
% 1.54/1.77 ((~b(s(z), z)) <=> (~b(s(z), elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[406])).
% 1.54/1.77 tff(6440,plain,
% 1.54/1.77 (~b(s(z), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1989, 6439])).
% 1.54/1.77 tff(6441,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[847, 6440])).
% 1.54/1.77 tff(6442,plain,((~(elem!1 = z)) | (~b(s(z), elem!1)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6443,plain,
% 1.54/1.77 (~(elem!1 = z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6442, 1989, 847])).
% 1.54/1.77 tff(6444,plain,
% 1.54/1.77 (~(z = elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[445, 6443])).
% 1.54/1.77 tff(6445,plain,
% 1.54/1.77 (b(z, elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1044, 6444, 1052])).
% 1.54/1.77 tff(6446,plain,
% 1.54/1.77 (~r(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2263, 77, 3406, 66])).
% 1.54/1.77 tff(6447,plain,
% 1.54/1.77 (b(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[391, 21, 388, 6446])).
% 1.54/1.77 tff(6448,plain,
% 1.54/1.77 (~r(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2075, 1331, 155, 1055, 1046, 847])).
% 1.54/1.77 tff(6449,plain,
% 1.54/1.77 (b(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[545, 6448, 439])).
% 1.54/1.77 tff(6450,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6451,plain,
% 1.54/1.77 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6452,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6451])).
% 1.54/1.77 tff(6453,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[6452, 6450])).
% 1.54/1.77 tff(6454,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(6455,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6454, 6453])).
% 1.54/1.77 tff(6456,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6455, 116, 1055, 6449, 847, 1331, 1048])).
% 1.54/1.77 tff(6457,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (elem!1 = z) | (~r(s(z), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(6458,plain,
% 1.54/1.77 (~b(s(s(z)), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6457, 6447, 847, 6445, 6443, 3406, 3670])).
% 1.54/1.77 tff(6459,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2285, 3406, 66])).
% 1.54/1.77 tff(6460,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[247, 6459])).
% 1.54/1.77 tff(6461,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.54/1.77 tff(6462,plain,
% 1.54/1.77 (r(s(s(z)), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[105, 6461])).
% 1.54/1.77 tff(6463,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)],[5016, 6462, 3953])).
% 1.54/1.77 tff(6464,plain,
% 1.54/1.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[5006, 77, 6462, 3953])).
% 1.54/1.77 tff(6465,plain,
% 1.54/1.77 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[149, 6464])).
% 1.54/1.77 tff(6466,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4984, 77, 6462, 3953])).
% 1.54/1.77 tff(6467,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[226, 6466])).
% 1.54/1.77 tff(6468,plain,
% 1.54/1.77 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3519, 116, 6467, 6465, 173])).
% 1.54/1.77 tff(6469,plain,
% 1.54/1.77 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[325, 6468])).
% 1.54/1.77 tff(6470,plain,
% 1.54/1.77 (~r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3975, 6469, 3953])).
% 1.54/1.77 tff(6471,plain,
% 1.54/1.77 (b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[194, 6470])).
% 1.54/1.77 tff(6472,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(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))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6473,plain,
% 1.54/1.77 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(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))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(6474,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(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)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[6473])).
% 1.54/1.77 tff(6475,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(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))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[6474, 6472])).
% 1.54/1.77 tff(6476,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(6477,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(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)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[6476, 6475])).
% 1.54/1.77 tff(6478,plain,
% 1.54/1.77 (~b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6477, 116, 1055, 2247, 6471, 6463])).
% 1.54/1.77 tff(6479,plain,
% 1.54/1.77 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[5816, 21, 6478])).
% 1.54/1.77 tff(6480,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6479, 5783])).
% 1.54/1.77 tff(6481,plain,
% 1.54/1.77 (~b(s(s(z)), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[6457, 4978, 847, 1055, 439, 155, 3670])).
% 1.54/1.77 tff(6482,plain,
% 1.54/1.77 (~b(elem!1, z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[5469, 1332, 2247, 1055])).
% 1.54/1.77 tff(6483,plain,
% 1.54/1.78 (r(elem!1, z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[545, 6482, 439])).
% 1.54/1.78 tff(6484,plain,
% 1.54/1.78 (~r(elem!1, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3015, 77, 6483, 66])).
% 1.54/1.78 tff(6485,plain,
% 1.54/1.78 (~r(elem!1, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[628, 6483, 155])).
% 1.54/1.78 tff(6486,plain,
% 1.54/1.78 (b(elem!1, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[633, 6485, 1046])).
% 1.54/1.78 tff(6487,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6488,plain,
% 1.54/1.78 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6489,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6488])).
% 1.54/1.78 tff(6490,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[6489, 6487])).
% 1.54/1.78 tff(6491,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(6492,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6491, 6490])).
% 1.54/1.78 tff(6493,plain,
% 1.54/1.78 (~b(elem!1, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6492, 116, 847, 6486, 1332, 4978])).
% 1.54/1.78 tff(6494,plain,
% 1.54/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6495,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(6496,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6495, 6494])).
% 1.54/1.78 tff(6497,plain,
% 1.54/1.78 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6496, 21])).
% 1.54/1.78 tff(6498,plain,
% 1.54/1.78 (elem!1 = s(s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6497, 6493, 6484])).
% 1.54/1.78 tff(6499,plain,
% 1.54/1.78 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6498])).
% 1.54/1.78 tff(6500,plain,
% 1.54/1.78 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[6499])).
% 1.54/1.78 tff(6501,plain,
% 1.54/1.78 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6500])).
% 1.54/1.78 tff(6502,plain,
% 1.54/1.78 (~b(elem!1, s(s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6461, 6501])).
% 1.54/1.78 tff(6503,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1332, 6502])).
% 1.54/1.78 tff(6504,plain,((~b(elem!1, s(s(s(z))))) | b(s(s(z)), s(s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (~r(s(z), z)) | (elem!1 = z) | (~b(s(s(s(z))), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(6505,plain,
% 1.54/1.78 (~b(elem!1, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6504, 6461, 66, 847, 3670, 155, 439, 2247, 1055])).
% 1.54/1.78 tff(6506,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6507,plain,
% 1.54/1.78 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6508,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6507])).
% 1.54/1.78 tff(6509,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[6508, 6506])).
% 1.54/1.78 tff(6510,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(6511,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6510, 6509])).
% 1.54/1.78 tff(6512,plain,
% 1.54/1.78 (~b(z, s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6511, 116, 271, 2247, 175, 1048])).
% 1.54/1.78 tff(6513,plain,
% 1.54/1.78 (b(z, s(s(z))) <=> b(z, elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[370])).
% 1.54/1.78 tff(6514,plain,
% 1.54/1.78 (b(z, elem!1) <=> b(z, s(s(z)))),
% 1.54/1.78 inference(symmetry,[status(thm)],[6513])).
% 1.54/1.78 tff(6515,plain,
% 1.54/1.78 (b(z, s(s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1055, 6514])).
% 1.54/1.78 tff(6516,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(6517,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6516, 6515])).
% 1.54/1.78 tff(6518,plain,((~(s(s(z)) = elem!1)) | b(z, s(s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(6519,plain,
% 1.54/1.78 (~(s(s(z)) = elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6518, 6512, 1055])).
% 1.54/1.78 tff(6520,plain,
% 1.54/1.78 (r(s(s(z)), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[426, 6519, 1])).
% 1.54/1.78 tff(6521,plain,
% 1.54/1.78 (~r(elem!1, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[5025, 6520, 2235])).
% 1.54/1.78 tff(6522,plain,
% 1.54/1.78 (elem!1 = s(s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1345, 6521, 1355])).
% 1.54/1.78 tff(6523,plain,
% 1.54/1.78 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6522])).
% 1.54/1.78 tff(6524,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1055, 6523])).
% 1.54/1.78 tff(6525,plain,
% 1.54/1.78 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6526,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6525])).
% 1.54/1.78 tff(6527,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[6526, 5822])).
% 1.54/1.78 tff(6528,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(6529,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6528, 6527])).
% 1.54/1.78 tff(6530,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6529, 116, 271, 2247, 6524, 175])).
% 1.54/1.78 tff(6531,plain,((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | b(elem!1, s(s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(z)), elem!1) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(6532,plain,
% 1.54/1.78 (~b(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6531, 6471, 2247, 1055, 6505, 6462, 6481, 4978])).
% 1.54/1.78 tff(6533,plain,
% 1.54/1.78 (r(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[289, 6532])).
% 1.54/1.78 tff(6534,plain,
% 1.54/1.78 (~r(s(s(s(s(s(z))))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[5835, 77, 6533, 6480])).
% 1.54/1.78 tff(6535,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[898, 21, 895, 6534])).
% 1.54/1.78 tff(6536,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6537,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6538,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6537])).
% 1.54/1.78 tff(6539,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[6538, 6536])).
% 1.54/1.78 tff(6540,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(6541,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6540, 6539])).
% 1.54/1.78 tff(6542,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6541, 116, 6467, 6465, 173])).
% 1.54/1.78 tff(6543,plain,
% 1.54/1.78 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2054, 21, 6542])).
% 1.54/1.78 tff(6544,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6543, 2044])).
% 1.54/1.78 tff(6545,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6546,plain,
% 1.54/1.78 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6547,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6546])).
% 1.54/1.78 tff(6548,plain,
% 1.54/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[6547, 6545])).
% 1.54/1.78 tff(6549,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(6550,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6549, 6548])).
% 1.54/1.78 tff(6551,plain,
% 1.54/1.78 (~r(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6550, 77, 6533, 3953, 6544])).
% 1.54/1.78 tff(6552,plain,
% 1.54/1.78 (b(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1576, 21, 6551, 1563])).
% 1.54/1.78 tff(6553,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4883, 6552, 6535, 2247, 5769, 3953])).
% 1.54/1.78 tff(6554,plain,(b(s(s(z)), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, elem!1)) | (~r(s(s(z)), z)) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(6555,plain,
% 1.54/1.78 (b(s(s(z)), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6554, 6445, 3953, 2247, 66, 847, 3406, 6443])).
% 1.54/1.78 tff(6556,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4668, 77, 3953, 292])).
% 1.54/1.78 tff(6557,plain,
% 1.54/1.78 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2054, 21, 6556])).
% 1.54/1.78 tff(6558,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6557, 2044])).
% 1.54/1.78 tff(6559,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6560,plain,
% 1.54/1.78 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(6561,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[6560])).
% 1.54/1.78 tff(6562,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[6561, 6559])).
% 1.54/1.78 tff(6563,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(6564,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[6563, 6562])).
% 1.54/1.78 tff(6565,plain,
% 1.54/1.78 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6564, 116, 27, 1048, 174, 6558])).
% 1.54/1.78 tff(6566,plain,
% 1.54/1.78 (r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[149, 6565])).
% 1.54/1.78 tff(6567,plain,
% 1.54/1.78 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[267, 21, 3333])).
% 1.54/1.78 tff(6568,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[6567, 253])).
% 1.54/1.78 tff(6569,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6570,plain,
% 1.54/1.79 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6571,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6570])).
% 1.54/1.79 tff(6572,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[6571, 6569])).
% 1.54/1.79 tff(6573,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(6574,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6573, 6572])).
% 1.54/1.79 tff(6575,plain,
% 1.54/1.79 (~b(z, s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6574, 116, 1055, 2247, 6568, 27])).
% 1.54/1.79 tff(6576,plain,
% 1.54/1.79 (~(s(s(z)) = elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6518, 6575, 1055])).
% 1.54/1.79 tff(6577,plain,
% 1.54/1.79 (r(s(s(z)), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[426, 6576, 1])).
% 1.54/1.79 tff(6578,plain,
% 1.54/1.79 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[437, 6577, 6566])).
% 1.54/1.79 tff(6579,plain,
% 1.54/1.79 (~r(elem!1, z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2105, 6576, 847, 1055, 254, 6558, 3670, 66])).
% 1.54/1.79 tff(6580,plain,
% 1.54/1.79 (b(elem!1, z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[545, 6579, 439])).
% 1.54/1.79 tff(6581,plain,
% 1.54/1.79 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1063, 6580, 254, 1055])).
% 1.54/1.79 tff(6582,plain,
% 1.54/1.79 (elem!1 = s(s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1068, 6581, 6578])).
% 1.54/1.79 tff(6583,plain,
% 1.54/1.79 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6582])).
% 1.54/1.79 tff(6584,plain,
% 1.54/1.79 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.54/1.79 inference(symmetry,[status(thm)],[6583])).
% 1.54/1.79 tff(6585,plain,
% 1.54/1.79 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, elem!1))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6584])).
% 1.54/1.79 tff(6586,plain,
% 1.54/1.79 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[267, 21, 2486])).
% 1.54/1.79 tff(6587,plain,
% 1.54/1.79 (b(z, s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6586, 253])).
% 1.54/1.79 tff(6588,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6589,plain,
% 1.54/1.79 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6590,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6589])).
% 1.54/1.79 tff(6591,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[6590, 6588])).
% 1.54/1.79 tff(6592,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(6593,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6592, 6591])).
% 1.54/1.79 tff(6594,plain,
% 1.54/1.79 (~b(z, s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6593, 116, 2247, 6587, 27])).
% 1.54/1.79 tff(6595,plain,
% 1.54/1.79 (r(z, s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1174, 6594])).
% 1.54/1.79 tff(6596,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5896, 6595, 293, 4867])).
% 1.54/1.79 tff(6597,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.54/1.79 tff(6598,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6599,plain,
% 1.54/1.79 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6600,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6599])).
% 1.54/1.79 tff(6601,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[6600, 6598])).
% 1.54/1.79 tff(6602,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(6603,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6602, 6601])).
% 1.54/1.79 tff(6604,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6603, 116, 27, 1048, 174, 5151, 6597])).
% 1.54/1.79 tff(6605,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(6606,plain,
% 1.54/1.79 (~b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6605, 6596, 1048, 174, 27])).
% 1.54/1.79 tff(6607,plain,
% 1.54/1.79 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5816, 21, 6606])).
% 1.54/1.79 tff(6608,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6607, 5783])).
% 1.54/1.79 tff(6609,plain,
% 1.54/1.79 (~r(s(s(s(s(s(z))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[5835, 77, 293, 6608])).
% 1.54/1.79 tff(6610,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[898, 21, 895, 4867, 6609])).
% 1.54/1.79 tff(6611,plain,(b(s(s(s(s(s(z))))), z) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(6612,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6611, 293, 1048, 174, 27, 2247, 3333])).
% 1.54/1.79 tff(6613,plain,
% 1.54/1.79 (~b(z, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4883, 6612, 2247, 254, 3953])).
% 1.54/1.79 tff(6614,plain,
% 1.54/1.79 (~b(z, elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6613, 6585])).
% 1.54/1.79 tff(6615,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1055, 6614])).
% 1.54/1.79 tff(6616,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | (~b(s(z), elem!1)) | (~r(s(s(z)), z)) | b(s(s(z)), elem!1) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(6617,plain,
% 1.54/1.79 (~r(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6616, 292, 254, 439, 847, 66, 1, 2247, 27, 3953, 1048, 174, 1055])).
% 1.54/1.79 tff(6618,plain,
% 1.54/1.79 (b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[289, 6617])).
% 1.54/1.79 tff(6619,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6620,plain,
% 1.54/1.79 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6621,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6620])).
% 1.54/1.79 tff(6622,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[6621, 6619])).
% 1.54/1.79 tff(6623,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(6624,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6623, 6622])).
% 1.54/1.79 tff(6625,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6624, 116, 6618, 27, 254, 174, 6558])).
% 1.54/1.79 tff(6626,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (elem!1 = z) | (~b(s(z), elem!1)) | (~r(s(s(z)), z)) | b(s(s(z)), elem!1) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(6627,plain,
% 1.54/1.79 (~r(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6626, 6555, 6460, 6438, 6443, 847, 66, 6458, 2247, 3953, 6447, 6445])).
% 1.54/1.79 tff(6628,plain,
% 1.54/1.79 (b(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[194, 6627])).
% 1.54/1.79 tff(6629,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3933, 116, 6445, 2247, 6555, 6628, 6438])).
% 1.54/1.79 tff(6630,plain,(b(s(z), z) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(6631,plain,
% 1.54/1.79 (r(z, elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6630, 1989, 6089, 26, 3952, 6436])).
% 1.54/1.79 tff(6632,plain,
% 1.54/1.79 (~r(s(s(z)), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[456, 6631, 26])).
% 1.54/1.79 tff(6633,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6634,plain,
% 1.54/1.79 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6635,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6634])).
% 1.54/1.79 tff(6636,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[6635, 6633])).
% 1.54/1.79 tff(6637,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(6638,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6637, 6636])).
% 1.54/1.79 tff(6639,plain,
% 1.54/1.79 (~b(s(s(s(s(z)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6638, 116, 271, 6020, 6558])).
% 1.54/1.79 tff(6640,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[247, 6639])).
% 1.54/1.79 tff(6641,plain,
% 1.54/1.79 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[237, 6640, 66])).
% 1.54/1.79 tff(6642,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[226, 6641])).
% 1.54/1.79 tff(6643,plain,
% 1.54/1.79 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.54/1.79 inference(symmetry,[status(thm)],[1393])).
% 1.54/1.79 tff(6644,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.54/1.79 tff(6645,plain,
% 1.54/1.79 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6644, 6643])).
% 1.54/1.79 tff(6646,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1708, 6645])).
% 1.54/1.79 tff(6647,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(6648,plain,
% 1.54/1.79 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6031, 6647])).
% 1.54/1.79 tff(6649,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)],[6648, 6642, 27, 3953, 292])).
% 1.54/1.79 tff(6650,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)],[1380, 6649])).
% 1.54/1.79 tff(6651,plain,
% 1.54/1.79 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6039, 116, 271, 2247, 27, 6650])).
% 1.54/1.79 tff(6652,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 6651])).
% 1.54/1.79 tff(6653,plain,
% 1.54/1.79 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3736, 77, 66, 6640])).
% 1.54/1.79 tff(6654,plain,
% 1.54/1.79 (b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[149, 6653])).
% 1.54/1.79 tff(6655,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6656,plain,
% 1.54/1.79 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6657,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6656])).
% 1.54/1.79 tff(6658,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[6657, 6655])).
% 1.54/1.79 tff(6659,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(6660,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[6659, 6658])).
% 1.54/1.79 tff(6661,plain,
% 1.54/1.79 (~b(s(z), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[6660, 116, 6642, 27, 6654, 6020])).
% 1.54/1.79 tff(6662,plain,
% 1.54/1.79 (r(s(z), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[172, 6661])).
% 1.54/1.79 tff(6663,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6664,plain,
% 1.54/1.79 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(6665,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[6664])).
% 1.54/1.79 tff(6666,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[6665, 6663])).
% 1.54/1.79 tff(6667,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(6668,plain,
% 1.54/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[6667, 6666])).
% 1.54/1.80 tff(6669,plain,
% 1.54/1.80 (~r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[6668, 77, 6662, 6652])).
% 1.54/1.80 tff(6670,plain,
% 1.54/1.80 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[5816, 21, 6669])).
% 1.54/1.80 tff(6671,plain,
% 1.54/1.80 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[6670, 5783])).
% 1.54/1.80 tff(6672,plain,
% 1.54/1.80 (~r(s(z), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[2285, 6640, 66])).
% 1.54/1.80 tff(6673,plain,
% 1.54/1.80 (b(s(z), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[210, 6672])).
% 1.54/1.80 tff(6674,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(6675,plain,
% 1.54/1.80 (((~b(z, s(z))) | (~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))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(6676,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[6675])).
% 1.54/1.80 tff(6677,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.80 inference(transitivity,[status(thm)],[6676, 6674])).
% 1.54/1.80 tff(6678,plain,
% 1.54/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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)))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(6679,plain,
% 1.54/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[6678, 6677])).
% 1.54/1.80 tff(6680,plain,
% 1.54/1.80 (~b(s(s(s(s(s(z))))), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[6679, 116, 6673, 271, 6671])).
% 1.54/1.80 tff(6681,plain,
% 1.54/1.80 (r(s(s(s(s(s(z))))), z)),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[898, 21, 895, 6680])).
% 1.54/1.80 tff(6682,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6683,plain,
% 1.64/1.80 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6684,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6683])).
% 1.64/1.80 tff(6685,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[6684, 6682])).
% 1.64/1.80 tff(6686,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(6687,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6686, 6685])).
% 1.64/1.80 tff(6688,plain,
% 1.64/1.80 (~b(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6687, 116, 271, 6020, 6558])).
% 1.64/1.80 tff(6689,plain,
% 1.64/1.80 (r(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1576, 21, 6688, 1563])).
% 1.64/1.80 tff(6690,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6691,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(6692,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6691, 6690])).
% 1.64/1.80 tff(6693,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)],[6692, 116, 6673, 271, 6558, 6671])).
% 1.64/1.80 tff(6694,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1405, 6647])).
% 1.64/1.80 tff(6695,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)],[6694, 6693])).
% 1.64/1.80 tff(6696,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6697,plain,
% 1.64/1.80 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), 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)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6698,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6697])).
% 1.64/1.80 tff(6699,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[6698, 6696])).
% 1.64/1.80 tff(6700,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(6701,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6700, 6699])).
% 1.64/1.80 tff(6702,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6701, 77, 6695, 6689, 6681])).
% 1.64/1.80 tff(6703,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(6704,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6703, 271, 27, 66, 2247, 3953])).
% 1.64/1.80 tff(6705,plain,
% 1.64/1.80 (b(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[194, 6704])).
% 1.64/1.80 tff(6706,plain,
% 1.64/1.80 (~b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3291, 6705, 2247, 271])).
% 1.64/1.80 tff(6707,plain,
% 1.64/1.80 (r(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[210, 6706])).
% 1.64/1.80 tff(6708,plain,
% 1.64/1.80 (~r(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[164, 6707, 66])).
% 1.64/1.80 tff(6709,plain,
% 1.64/1.80 (b(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[172, 6708])).
% 1.64/1.80 tff(6710,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6711,plain,
% 1.64/1.80 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6712,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6711])).
% 1.64/1.80 tff(6713,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[6712, 6710])).
% 1.64/1.80 tff(6714,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(6715,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6714, 6713])).
% 1.64/1.80 tff(6716,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6715, 116, 271, 2247, 27, 6705, 6709])).
% 1.64/1.80 tff(6717,plain,((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(6718,plain,
% 1.64/1.80 (~b(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6717, 27, 6436, 26, 3952])).
% 1.64/1.80 tff(6719,plain,
% 1.64/1.80 (r(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[289, 6718])).
% 1.64/1.80 tff(6720,plain,
% 1.64/1.80 (~r(s(s(z)), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3659, 6719, 26])).
% 1.64/1.80 tff(6721,plain,
% 1.64/1.80 (b(s(s(z)), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[391, 21, 388, 6720])).
% 1.64/1.80 tff(6722,plain,
% 1.64/1.80 (~r(elem!1, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[791, 6631, 6719])).
% 1.64/1.80 tff(6723,plain,
% 1.64/1.80 (b(elem!1, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[633, 6722, 6342])).
% 1.64/1.80 tff(6724,plain,
% 1.64/1.80 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6725,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6724])).
% 1.64/1.80 tff(6726,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[6725, 3709])).
% 1.64/1.80 tff(6727,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(6728,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6727, 6726])).
% 1.64/1.80 tff(6729,plain,
% 1.64/1.80 (~b(s(s(z)), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6728, 116, 6089, 6723, 6721])).
% 1.64/1.80 tff(6730,plain,
% 1.64/1.80 (s(s(z)) = elem!1),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[426, 6729, 6632])).
% 1.64/1.80 tff(6731,plain,
% 1.64/1.80 (s(s(s(z))) = s(elem!1)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6730])).
% 1.64/1.80 tff(6732,plain,
% 1.64/1.80 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6731])).
% 1.64/1.80 tff(6733,plain,
% 1.64/1.80 (~r(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[164, 3406, 26])).
% 1.64/1.80 tff(6734,plain,
% 1.64/1.80 (b(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[172, 6733])).
% 1.64/1.80 tff(6735,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2285, 3406, 26])).
% 1.64/1.80 tff(6736,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[247, 6735])).
% 1.64/1.80 tff(6737,plain,
% 1.64/1.80 (~(elem!1 = z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6442, 1989, 6089])).
% 1.64/1.80 tff(6738,plain,
% 1.64/1.80 (~(z = elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[445, 6737])).
% 1.64/1.80 tff(6739,plain,
% 1.64/1.80 (b(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3705, 6729, 6631, 6719, 6349, 6738, 2, 6736])).
% 1.64/1.80 tff(6740,plain,
% 1.64/1.80 (~b(s(s(s(s(s(z))))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4883, 6739, 6436, 6736, 3952])).
% 1.64/1.80 tff(6741,plain,
% 1.64/1.80 (r(z, s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6611, 6740, 27, 6719, 6734, 6436, 6721])).
% 1.64/1.80 tff(6742,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[301, 6741, 6719])).
% 1.64/1.80 tff(6743,plain,
% 1.64/1.80 (b(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[194, 6742])).
% 1.64/1.80 tff(6744,plain,
% 1.64/1.80 (b(s(z), s(elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6743, 6732])).
% 1.64/1.80 tff(6745,plain,
% 1.64/1.80 (s(elem!1) = s(s(s(z)))),
% 1.64/1.80 inference(symmetry,[status(thm)],[6731])).
% 1.64/1.80 tff(6746,plain,
% 1.64/1.80 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6745])).
% 1.64/1.80 tff(6747,plain,
% 1.64/1.80 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.64/1.80 inference(symmetry,[status(thm)],[6746])).
% 1.64/1.80 tff(6748,plain,
% 1.64/1.80 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6730])).
% 1.64/1.80 tff(6749,plain,
% 1.64/1.80 (b(elem!1, s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[27, 6748])).
% 1.64/1.80 tff(6750,plain,
% 1.64/1.80 (b(elem!1, s(elem!1))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6749, 6747])).
% 1.64/1.80 tff(6751,plain,
% 1.64/1.80 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6731])).
% 1.64/1.80 tff(6752,plain,
% 1.64/1.80 (b(s(elem!1), z)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6436, 6751])).
% 1.64/1.80 tff(6753,plain,
% 1.64/1.80 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6731])).
% 1.64/1.80 tff(6754,plain,
% 1.64/1.80 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6753])).
% 1.64/1.80 tff(6755,plain,
% 1.64/1.80 (b(z, s(s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6739, 6754])).
% 1.64/1.80 tff(6756,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6757,plain,
% 1.64/1.80 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6758,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6757])).
% 1.64/1.80 tff(6759,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[6758, 6756])).
% 1.64/1.80 tff(6760,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(6761,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[6760, 6759])).
% 1.64/1.80 tff(6762,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6761, 116, 6089, 6755, 6752, 6750, 6744])).
% 1.64/1.80 tff(6763,plain,(b(s(z), z) | (~b(s(s(z)), s(s(s(z))))) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(6764,plain,
% 1.64/1.80 (b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6763, 27, 2])).
% 1.64/1.80 tff(6765,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4668, 77, 3952, 6090])).
% 1.64/1.80 tff(6766,plain,
% 1.64/1.80 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2054, 21, 6765])).
% 1.64/1.80 tff(6767,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6766, 2044])).
% 1.64/1.80 tff(6768,plain,
% 1.64/1.80 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3975, 6090, 3952])).
% 1.64/1.80 tff(6769,plain,
% 1.64/1.80 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[325, 6768])).
% 1.64/1.80 tff(6770,plain,
% 1.64/1.80 (~r(s(s(z)), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3659, 293, 26])).
% 1.64/1.80 tff(6771,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 1.64/1.80 tff(6772,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[391, 21, 4432, 388, 6771])).
% 1.64/1.80 tff(6773,plain,(b(s(s(z)), s(z)) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(6774,plain,
% 1.64/1.80 (b(s(s(z)), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[6773, 6770])).
% 1.64/1.80 tff(6775,plain,
% 1.64/1.80 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(6776,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[6775])).
% 1.64/1.80 tff(6777,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6776, 3877])).
% 1.64/1.81 tff(6778,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(6779,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6778, 6777])).
% 1.64/1.81 tff(6780,plain,
% 1.64/1.81 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6779, 116, 6774, 6769, 6767])).
% 1.64/1.81 tff(6781,plain,
% 1.64/1.81 (r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[226, 6780])).
% 1.64/1.81 tff(6782,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[237, 6781, 26])).
% 1.64/1.81 tff(6783,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[247, 6782])).
% 1.64/1.81 tff(6784,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6785,plain,
% 1.64/1.81 (((~b(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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6786,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6785])).
% 1.64/1.81 tff(6787,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6786, 6784])).
% 1.64/1.81 tff(6788,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(6789,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6788, 6787])).
% 1.64/1.81 tff(6790,plain,
% 1.64/1.81 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6789, 116, 6774, 6769, 6767])).
% 1.64/1.81 tff(6791,plain,
% 1.64/1.81 (r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[149, 6790])).
% 1.64/1.81 tff(6792,plain,
% 1.64/1.81 (r(z, elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6099, 518, 6089, 293, 270])).
% 1.64/1.81 tff(6793,plain,
% 1.64/1.81 (b(s(s(z)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1039, 6792, 2, 328, 254, 518])).
% 1.64/1.81 tff(6794,plain,
% 1.64/1.81 (~r(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[791, 6792, 293])).
% 1.64/1.81 tff(6795,plain,
% 1.64/1.81 (b(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[633, 6794, 6342])).
% 1.64/1.81 tff(6796,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3714, 116, 6089, 6795, 6793, 6774])).
% 1.64/1.81 tff(6797,plain,((z = elem!1) | b(s(s(z)), z) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(6798,plain,
% 1.64/1.81 (z = elem!1),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6797, 6791, 2, 6783, 293, 270])).
% 1.64/1.81 tff(6799,plain,
% 1.64/1.81 (elem!1 = z),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[445, 6798])).
% 1.64/1.81 tff(6800,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2421, 6799, 6782])).
% 1.64/1.81 tff(6801,plain,
% 1.64/1.81 (~r(z, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[301, 6090, 293])).
% 1.64/1.81 tff(6802,plain,
% 1.64/1.81 (~r(elem!1, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2488, 6799, 6801])).
% 1.64/1.81 tff(6803,plain,
% 1.64/1.81 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4113, 6802, 3946])).
% 1.64/1.81 tff(6804,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1596, 6803, 6800])).
% 1.64/1.81 tff(6805,plain,
% 1.64/1.81 (s(z) = s(elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6798])).
% 1.64/1.81 tff(6806,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6805])).
% 1.64/1.81 tff(6807,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6767, 6806])).
% 1.64/1.81 tff(6808,plain,
% 1.64/1.81 (b(s(elem!1), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6119, 6798, 6089])).
% 1.64/1.81 tff(6809,plain,
% 1.64/1.81 (~(elem!1 = s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1667, 1664, 6089])).
% 1.64/1.81 tff(6810,plain,
% 1.64/1.81 (b(elem!1, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1345, 6802, 6809])).
% 1.64/1.81 tff(6811,plain,
% 1.64/1.81 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6798])).
% 1.64/1.81 tff(6812,plain,
% 1.64/1.81 (b(s(s(s(z))), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6436, 6811])).
% 1.64/1.81 tff(6813,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6814,plain,
% 1.64/1.81 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6815,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6814])).
% 1.64/1.81 tff(6816,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6815, 6813])).
% 1.64/1.81 tff(6817,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(6818,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6817, 6816])).
% 1.64/1.81 tff(6819,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6818, 116, 6812, 6810, 6808, 6807, 6804])).
% 1.64/1.81 tff(6820,plain,(b(s(z), s(s(s(z)))) | b(s(s(z)), z) | (~r(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(6821,plain,
% 1.64/1.81 (b(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6820, 6719, 2, 6764])).
% 1.64/1.81 tff(6822,plain,
% 1.64/1.81 (z = elem!1),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6099, 3293, 847, 1052, 270])).
% 1.64/1.81 tff(6823,plain,
% 1.64/1.81 (s(z) = s(elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6822])).
% 1.64/1.81 tff(6824,plain,
% 1.64/1.81 (s(elem!1) = s(z)),
% 1.64/1.81 inference(symmetry,[status(thm)],[6823])).
% 1.64/1.81 tff(6825,plain,
% 1.64/1.81 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6824])).
% 1.64/1.81 tff(6826,plain,
% 1.64/1.81 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[6825])).
% 1.64/1.81 tff(6827,plain,
% 1.64/1.81 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[175, 6826])).
% 1.64/1.81 tff(6828,plain,
% 1.64/1.81 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6822])).
% 1.64/1.81 tff(6829,plain,
% 1.64/1.81 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6828, 1580])).
% 1.64/1.81 tff(6830,plain,
% 1.64/1.81 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.81 inference(transitivity,[status(thm)],[6829, 3575])).
% 1.64/1.81 tff(6831,plain,
% 1.64/1.81 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6830])).
% 1.64/1.81 tff(6832,plain,
% 1.64/1.81 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[242, 6831])).
% 1.64/1.81 tff(6833,plain,
% 1.64/1.81 (elem!1 = z),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[445, 6822])).
% 1.64/1.81 tff(6834,plain,
% 1.64/1.81 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6822])).
% 1.64/1.81 tff(6835,plain,
% 1.64/1.81 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.64/1.81 inference(symmetry,[status(thm)],[6834])).
% 1.64/1.81 tff(6836,plain,
% 1.64/1.81 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6835])).
% 1.64/1.81 tff(6837,plain,
% 1.64/1.81 (~b(elem!1, z)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3544, 6836])).
% 1.64/1.81 tff(6838,plain,
% 1.64/1.81 (~(elem!1 = s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2407, 6837, 2247])).
% 1.64/1.81 tff(6839,plain,
% 1.64/1.81 (b(s(elem!1), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6119, 6822, 847])).
% 1.64/1.81 tff(6840,plain,
% 1.64/1.81 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6822])).
% 1.64/1.81 tff(6841,plain,
% 1.64/1.81 (b(s(s(s(z))), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[2247, 6840])).
% 1.64/1.81 tff(6842,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.64/1.81 tff(6843,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6844,plain,
% 1.64/1.81 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6845,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6844])).
% 1.64/1.81 tff(6846,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6845, 6843])).
% 1.64/1.81 tff(6847,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(6848,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6847, 6846])).
% 1.64/1.81 tff(6849,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6848, 116, 3561, 1332, 846, 6842])).
% 1.64/1.81 tff(6850,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(6851,plain,
% 1.64/1.81 (~b(elem!1, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6850, 6841, 6839, 6827])).
% 1.64/1.81 tff(6852,plain,
% 1.64/1.81 (r(elem!1, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1345, 6851, 6838])).
% 1.64/1.81 tff(6853,plain,
% 1.64/1.81 (r(z, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2488, 6852, 6833])).
% 1.64/1.81 tff(6854,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5649, 6853, 3953])).
% 1.64/1.81 tff(6855,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2421, 6854, 6833])).
% 1.64/1.81 tff(6856,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1596, 6855, 6832])).
% 1.64/1.81 tff(6857,plain,
% 1.64/1.81 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6829])).
% 1.64/1.81 tff(6858,plain,
% 1.64/1.81 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[242, 6857])).
% 1.64/1.81 tff(6859,plain,
% 1.64/1.81 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4401, 77, 3953, 6852])).
% 1.64/1.81 tff(6860,plain,
% 1.64/1.81 (b(elem!1, s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1068, 6859, 6858])).
% 1.64/1.81 tff(6861,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6862,plain,
% 1.64/1.81 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6863,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6862])).
% 1.64/1.81 tff(6864,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6863, 6861])).
% 1.64/1.81 tff(6865,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(6866,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6865, 6864])).
% 1.64/1.81 tff(6867,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6866, 116, 6841, 6860, 6839, 6856, 6827])).
% 1.64/1.81 tff(6868,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), elem!1)) | r(z, elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(6869,plain,
% 1.64/1.81 (r(z, elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6868, 6821, 6089, 6436, 3952, 6764])).
% 1.64/1.81 tff(6870,plain,
% 1.64/1.81 (~r(s(s(z)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[456, 6869, 26])).
% 1.64/1.81 tff(6871,plain,
% 1.64/1.81 (~(elem!1 = z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1685, 6870, 2])).
% 1.64/1.81 tff(6872,plain,
% 1.64/1.81 (~(z = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[445, 6871])).
% 1.64/1.81 tff(6873,plain,
% 1.64/1.81 (b(s(s(z)), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6773, 6720])).
% 1.64/1.81 tff(6874,plain,
% 1.64/1.81 (~r(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[791, 6869, 6719])).
% 1.64/1.81 tff(6875,plain,
% 1.64/1.81 (b(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[633, 6874, 6342])).
% 1.64/1.81 tff(6876,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6877,plain,
% 1.64/1.81 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6878,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6877])).
% 1.64/1.81 tff(6879,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6878, 6876])).
% 1.64/1.81 tff(6880,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(6881,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6880, 6879])).
% 1.64/1.81 tff(6882,plain,
% 1.64/1.81 (~b(s(s(z)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6881, 116, 6875, 6436, 6821, 6873])).
% 1.64/1.81 tff(6883,plain,
% 1.64/1.81 (s(s(z)) = elem!1),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[426, 6882, 6870])).
% 1.64/1.81 tff(6884,plain,
% 1.64/1.81 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[529, 6883, 6872])).
% 1.64/1.81 tff(6885,plain,
% 1.64/1.81 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2182, 6884])).
% 1.64/1.81 tff(6886,plain,
% 1.64/1.81 (s(s(s(z))) = s(elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6883])).
% 1.64/1.81 tff(6887,plain,
% 1.64/1.81 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6886])).
% 1.64/1.81 tff(6888,plain,
% 1.64/1.81 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[6887])).
% 1.64/1.81 tff(6889,plain,
% 1.64/1.81 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6886])).
% 1.64/1.81 tff(6890,plain,
% 1.64/1.81 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6889, 6886])).
% 1.64/1.81 tff(6891,plain,
% 1.64/1.81 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6890, 6888])).
% 1.64/1.81 tff(6892,plain,
% 1.64/1.81 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3952, 6891])).
% 1.64/1.81 tff(6893,plain,
% 1.64/1.81 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6883])).
% 1.64/1.81 tff(6894,plain,
% 1.64/1.81 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.81 inference(transitivity,[status(thm)],[6893, 591])).
% 1.64/1.81 tff(6895,plain,
% 1.64/1.81 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6894])).
% 1.64/1.81 tff(6896,plain,
% 1.64/1.81 (~(s(s(s(z))) = elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[100, 6895])).
% 1.64/1.81 tff(6897,plain,
% 1.64/1.81 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6883])).
% 1.64/1.81 tff(6898,plain,
% 1.64/1.81 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6897])).
% 1.64/1.81 tff(6899,plain,
% 1.64/1.81 (b(s(z), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2038, 6883, 6089])).
% 1.64/1.81 tff(6900,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[184, 6899, 27, 6821])).
% 1.64/1.81 tff(6901,plain,
% 1.64/1.81 (~b(s(s(s(z))), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6900, 6898])).
% 1.64/1.81 tff(6902,plain,
% 1.64/1.81 (r(s(s(s(z))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2725, 6901, 6896])).
% 1.64/1.81 tff(6903,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6904,plain,
% 1.64/1.81 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(6905,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6904])).
% 1.64/1.81 tff(6906,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[6905, 6903])).
% 1.64/1.81 tff(6907,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(6908,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 1.64/1.81 tff(6909,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6908, 77, 752, 2608, 638])).
% 1.64/1.81 tff(6910,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(6911,plain,
% 1.64/1.81 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[6910, 6902, 6892])).
% 1.64/1.81 tff(6912,plain,
% 1.64/1.81 (b(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[743, 6911, 6884])).
% 1.64/1.81 tff(6913,plain,
% 1.64/1.81 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[912, 6883])).
% 1.64/1.81 tff(6914,plain,
% 1.64/1.81 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[568, 6883])).
% 1.64/1.81 tff(6915,plain,
% 1.64/1.81 (~(s(elem!1) = s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[842, 6883])).
% 1.64/1.81 tff(6916,plain,
% 1.64/1.81 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[836, 6883, 6884])).
% 1.64/1.81 tff(6917,plain,
% 1.64/1.81 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[6886])).
% 1.64/1.82 tff(6918,plain,
% 1.64/1.82 (b(s(elem!1), z)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[6436, 6917])).
% 1.64/1.82 tff(6919,plain,
% 1.64/1.82 ((~r(s(s(s(s(s(z))))), elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~r(z, elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3807, 1901])).
% 1.64/1.82 tff(6920,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6919, 6918, 6764, 6869, 6916, 6915])).
% 1.64/1.82 tff(6921,plain,
% 1.64/1.82 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[885, 6920, 6914])).
% 1.64/1.82 tff(6922,plain,
% 1.64/1.82 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1004, 116, 616, 847, 667, 845])).
% 1.64/1.82 tff(6923,plain,
% 1.64/1.82 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[916, 21, 953, 6922])).
% 1.64/1.82 tff(6924,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[984, 77, 794, 871, 6923])).
% 1.64/1.82 tff(6925,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (s(z) = s(s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(6926,plain,
% 1.64/1.82 ((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6925, 1901])).
% 1.64/1.82 tff(6927,plain,
% 1.64/1.82 (~r(s(s(elem!1)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6926, 6921, 6089, 6913, 6875, 6912])).
% 1.64/1.82 tff(6928,plain,
% 1.64/1.82 (b(s(s(elem!1)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[808, 6927])).
% 1.64/1.82 tff(6929,plain,
% 1.64/1.82 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3698, 6928, 6089, 6912])).
% 1.64/1.82 tff(6930,plain,
% 1.64/1.82 (r(elem!1, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1892, 6929, 6885])).
% 1.64/1.82 tff(6931,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(6932,plain,
% 1.64/1.82 (((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(6933,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[6932])).
% 1.64/1.82 tff(6934,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[6933, 6931])).
% 1.64/1.82 tff(6935,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(6936,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[6935, 6934])).
% 1.64/1.82 tff(6937,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6936, 116, 1436, 616, 270, 668, 667])).
% 1.64/1.82 tff(6938,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(6939,plain,
% 1.64/1.82 (~b(z, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6938, 6928, 6764, 6875, 6912])).
% 1.64/1.82 tff(6940,plain,
% 1.64/1.82 (r(z, s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[514, 6939])).
% 1.64/1.82 tff(6941,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[502, 6940, 6930, 6869])).
% 1.64/1.82 tff(6942,plain,((~b(s(s(z)), s(s(s(z))))) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(6943,plain,
% 1.64/1.82 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6942, 2])).
% 1.64/1.82 tff(6944,plain,
% 1.64/1.82 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[105, 6943])).
% 1.64/1.82 tff(6945,plain,
% 1.64/1.82 (b(s(z), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6630, 1052, 6089, 26, 3952, 6436])).
% 1.64/1.82 tff(6946,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(6947,plain,
% 1.64/1.82 (((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(6948,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[6947])).
% 1.64/1.82 tff(6949,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[6948, 6946])).
% 1.64/1.82 tff(6950,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(6951,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[6950, 6949])).
% 1.64/1.82 tff(6952,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6951, 116, 847, 4986, 2329, 2321, 6020])).
% 1.64/1.82 tff(6953,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(6954,plain,
% 1.64/1.82 (~r(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6953, 2235, 6089, 3952])).
% 1.64/1.82 tff(6955,plain,
% 1.64/1.82 (b(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[194, 6954])).
% 1.64/1.82 tff(6956,plain,
% 1.64/1.82 (~b(z, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3291, 6955, 6436, 6945])).
% 1.64/1.82 tff(6957,plain,
% 1.64/1.82 (r(z, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[289, 6956])).
% 1.64/1.82 tff(6958,plain,
% 1.64/1.82 (z = elem!1),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6099, 6957, 6089, 1052, 6945])).
% 1.64/1.82 tff(6959,plain,
% 1.64/1.82 (s(z) = s(elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[6958])).
% 1.64/1.82 tff(6960,plain,
% 1.64/1.82 (s(elem!1) = s(z)),
% 1.64/1.82 inference(symmetry,[status(thm)],[6959])).
% 1.64/1.82 tff(6961,plain,
% 1.64/1.82 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[6960])).
% 1.64/1.82 tff(6962,plain,
% 1.64/1.82 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[6961])).
% 1.64/1.82 tff(6963,plain,
% 1.64/1.82 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[6955, 6962])).
% 1.64/1.82 tff(6964,plain,
% 1.64/1.82 (b(s(elem!1), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6119, 6958, 6089])).
% 1.64/1.82 tff(6965,plain,
% 1.64/1.82 (elem!1 = z),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[445, 6958])).
% 1.64/1.82 tff(6966,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2488, 6965, 5112])).
% 1.64/1.82 tff(6967,plain,
% 1.64/1.82 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[6958])).
% 1.64/1.82 tff(6968,plain,
% 1.64/1.82 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.64/1.82 inference(symmetry,[status(thm)],[6967])).
% 1.64/1.82 tff(6969,plain,
% 1.64/1.82 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[6968])).
% 1.64/1.82 tff(6970,plain,
% 1.64/1.82 (~b(elem!1, z)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[3544, 6969])).
% 1.64/1.82 tff(6971,plain,
% 1.64/1.82 (~(elem!1 = s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2407, 6970, 6436])).
% 1.64/1.82 tff(6972,plain,
% 1.64/1.82 (b(elem!1, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1345, 6971, 6966])).
% 1.64/1.82 tff(6973,plain,
% 1.64/1.82 (~(s(s(s(z))) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1749, 6958])).
% 1.64/1.82 tff(6974,plain,
% 1.64/1.82 (r(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1685, 6965, 2])).
% 1.64/1.82 tff(6975,plain,
% 1.64/1.82 (~r(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4976, 6974, 2235])).
% 1.64/1.82 tff(6976,plain,
% 1.64/1.82 (b(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2725, 6975, 6973])).
% 1.64/1.82 tff(6977,plain,
% 1.64/1.82 (~b(s(elem!1), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6848, 116, 6976, 6972, 6964])).
% 1.64/1.82 tff(6978,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6977, 6963])).
% 1.64/1.82 tff(6979,plain,((~r(s(s(z)), s(s(s(z))))) | b(s(s(z)), z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(6980,plain,
% 1.64/1.82 (r(z, elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6979, 6944, 2])).
% 1.64/1.82 tff(6981,plain,
% 1.64/1.82 (~r(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[456, 6980, 26])).
% 1.64/1.82 tff(6982,plain,
% 1.64/1.82 (~r(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6953, 6944, 6089, 3952])).
% 1.64/1.82 tff(6983,plain,
% 1.64/1.82 (b(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[194, 6982])).
% 1.64/1.82 tff(6984,plain,
% 1.64/1.82 (~r(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2263, 77, 155, 26])).
% 1.64/1.82 tff(6985,plain,
% 1.64/1.82 (b(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6773, 6984])).
% 1.64/1.82 tff(6986,plain,
% 1.64/1.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5006, 77, 6944, 3952])).
% 1.64/1.82 tff(6987,plain,
% 1.64/1.82 (b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[149, 6986])).
% 1.64/1.82 tff(6988,plain,
% 1.64/1.82 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4984, 77, 6944, 3952])).
% 1.64/1.82 tff(6989,plain,
% 1.64/1.82 (b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[226, 6988])).
% 1.64/1.82 tff(6990,plain,
% 1.64/1.82 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5016, 6944, 3952])).
% 1.64/1.82 tff(6991,plain,
% 1.64/1.82 (~r(s(z), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[164, 155, 26])).
% 1.64/1.82 tff(6992,plain,
% 1.64/1.82 (b(s(z), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[172, 6991])).
% 1.64/1.82 tff(6993,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(6994,plain,
% 1.64/1.82 (((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(6995,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[6994])).
% 1.64/1.82 tff(6996,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[6995, 6993])).
% 1.64/1.82 tff(6997,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(6998,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[6997, 6996])).
% 1.64/1.82 tff(6999,plain,
% 1.64/1.82 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6998, 116, 6089, 6989, 6985, 6992])).
% 1.64/1.82 tff(7000,plain,
% 1.64/1.82 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2054, 21, 6999])).
% 1.64/1.82 tff(7001,plain,
% 1.64/1.82 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7000, 2044])).
% 1.64/1.82 tff(7002,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7003,plain,
% 1.64/1.82 (((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7004,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7003])).
% 1.64/1.82 tff(7005,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[7004, 7002])).
% 1.64/1.82 tff(7006,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7007,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7006, 7005])).
% 1.64/1.82 tff(7008,plain,
% 1.64/1.82 (~b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7007, 116, 271, 2247, 175, 5031])).
% 1.64/1.82 tff(7009,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5816, 21, 7008])).
% 1.64/1.82 tff(7010,plain,
% 1.64/1.82 (r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7009, 5783])).
% 1.64/1.82 tff(7011,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7012,plain,
% 1.64/1.82 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7013,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7012])).
% 1.64/1.82 tff(7014,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[7013, 7011])).
% 1.64/1.82 tff(7015,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7016,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[7015, 7014])).
% 1.64/1.82 tff(7017,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[7016, 77, 3953, 6153, 7010])).
% 1.64/1.82 tff(7018,plain,
% 1.64/1.82 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[6694, 7017])).
% 1.64/1.82 tff(7019,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7020,plain,
% 1.64/1.82 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(7021,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[7020])).
% 1.64/1.82 tff(7022,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[7021, 7019])).
% 1.64/1.82 tff(7023,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(7024,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7023, 7022])).
% 1.64/1.83 tff(7025,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7024, 116, 212, 2410, 7018])).
% 1.64/1.83 tff(7026,plain,
% 1.64/1.83 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 7025])).
% 1.64/1.83 tff(7027,plain,
% 1.64/1.83 (r(z, s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1174, 6512])).
% 1.64/1.83 tff(7028,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7029,plain,
% 1.64/1.83 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7030,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7029])).
% 1.64/1.83 tff(7031,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7030, 7028])).
% 1.64/1.83 tff(7032,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7033,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7032, 7031])).
% 1.64/1.83 tff(7034,plain,
% 1.64/1.83 (~r(s(s(s(s(s(z))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7033, 77, 448, 7027, 7026])).
% 1.64/1.83 tff(7035,plain,
% 1.64/1.83 (b(s(s(s(s(s(z))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[898, 21, 895, 7034])).
% 1.64/1.83 tff(7036,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7037,plain,
% 1.64/1.83 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7038,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7037])).
% 1.64/1.83 tff(7039,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7038, 7036])).
% 1.64/1.83 tff(7040,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7041,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7040, 7039])).
% 1.64/1.83 tff(7042,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7041, 116, 847, 271, 2247, 5031, 7035])).
% 1.64/1.83 tff(7043,plain,((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7044,plain,
% 1.64/1.83 (~b(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7043, 7001, 6436, 6990, 6980, 6989, 6987, 3952, 6089, 6983, 6985])).
% 1.64/1.83 tff(7045,plain,
% 1.64/1.83 (r(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[289, 7044])).
% 1.64/1.83 tff(7046,plain,
% 1.64/1.83 (~r(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[791, 7045, 6980])).
% 1.64/1.83 tff(7047,plain,
% 1.64/1.83 (b(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[633, 7046, 6342])).
% 1.64/1.83 tff(7048,plain,
% 1.64/1.83 (~b(s(s(z)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[6728, 116, 6089, 7047, 6985])).
% 1.64/1.83 tff(7049,plain,
% 1.64/1.83 (s(s(z)) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[426, 7048, 6981])).
% 1.64/1.83 tff(7050,plain,
% 1.64/1.83 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[568, 7049])).
% 1.64/1.83 tff(7051,plain,
% 1.64/1.83 (s(s(s(z))) = s(elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7049])).
% 1.64/1.83 tff(7052,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7051])).
% 1.64/1.83 tff(7053,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[7052])).
% 1.64/1.83 tff(7054,plain,
% 1.64/1.83 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7053])).
% 1.64/1.83 tff(7055,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[7054])).
% 1.64/1.83 tff(7056,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7049])).
% 1.64/1.83 tff(7057,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[6989, 7056])).
% 1.64/1.83 tff(7058,plain,
% 1.64/1.83 (b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7057, 7055])).
% 1.64/1.83 tff(7059,plain,
% 1.64/1.83 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[912, 7049])).
% 1.64/1.83 tff(7060,plain,
% 1.64/1.83 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7052])).
% 1.64/1.83 tff(7061,plain,
% 1.64/1.83 (r(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7001, 7060])).
% 1.64/1.83 tff(7062,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[6926, 7061, 6089, 7059, 7047, 7058])).
% 1.64/1.83 tff(7063,plain,
% 1.64/1.83 (r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[885, 7062, 7050])).
% 1.64/1.83 tff(7064,plain,
% 1.64/1.83 (~r(s(s(s(s(s(z))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[892, 77, 6980, 7063])).
% 1.64/1.83 tff(7065,plain,
% 1.64/1.83 (~r(s(s(s(s(z)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2285, 155, 26])).
% 1.64/1.83 tff(7066,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[247, 7065])).
% 1.64/1.83 tff(7067,plain,
% 1.64/1.83 (~(elem!1 = z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1685, 6981, 2])).
% 1.64/1.83 tff(7068,plain,
% 1.64/1.83 (~(z = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[445, 7067])).
% 1.64/1.83 tff(7069,plain,
% 1.64/1.83 (b(z, s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3705, 7048, 6980, 7066, 6349, 7068, 2, 7045])).
% 1.64/1.83 tff(7070,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4883, 7069, 6436, 7066, 3952])).
% 1.64/1.83 tff(7071,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[898, 21, 895, 7070, 7064])).
% 1.64/1.83 tff(7072,plain,((~r(s(z), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7073,plain,
% 1.64/1.83 (~r(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7072, 2])).
% 1.64/1.83 tff(7074,plain,
% 1.64/1.83 (b(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[210, 7073])).
% 1.64/1.83 tff(7075,plain,
% 1.64/1.83 (~b(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3291, 7074, 6436, 6983])).
% 1.64/1.83 tff(7076,plain,
% 1.64/1.83 (r(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[289, 7075])).
% 1.64/1.83 tff(7077,plain,
% 1.64/1.83 (~r(s(s(z)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3659, 7076, 26])).
% 1.64/1.83 tff(7078,plain,
% 1.64/1.83 (b(s(s(z)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[6773, 7077])).
% 1.64/1.83 tff(7079,plain,
% 1.64/1.83 (~r(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[791, 7076, 6980])).
% 1.64/1.83 tff(7080,plain,
% 1.64/1.83 (b(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[633, 7079, 6342])).
% 1.64/1.83 tff(7081,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3714, 116, 847, 667, 1331, 1048])).
% 1.64/1.83 tff(7082,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7083,plain,
% 1.64/1.83 (~b(s(s(z)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7082, 6089, 7080, 7078])).
% 1.64/1.83 tff(7084,plain,
% 1.64/1.83 (s(s(z)) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[426, 7083, 6981])).
% 1.64/1.83 tff(7085,plain,
% 1.64/1.83 (s(s(s(z))) = s(elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7084])).
% 1.64/1.83 tff(7086,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7085])).
% 1.64/1.83 tff(7087,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[7086])).
% 1.64/1.83 tff(7088,plain,
% 1.64/1.83 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7087])).
% 1.64/1.83 tff(7089,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[7088])).
% 1.64/1.83 tff(7090,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7084])).
% 1.64/1.83 tff(7091,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[6989, 7090])).
% 1.64/1.83 tff(7092,plain,
% 1.64/1.83 (b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7091, 7089])).
% 1.64/1.83 tff(7093,plain,
% 1.64/1.83 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[912, 7084])).
% 1.64/1.83 tff(7094,plain,
% 1.64/1.83 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7085])).
% 1.64/1.83 tff(7095,plain,
% 1.64/1.83 (b(s(z), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[6983, 7094])).
% 1.64/1.83 tff(7096,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7097,plain,
% 1.64/1.83 (((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7098,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7097])).
% 1.64/1.83 tff(7099,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7098, 7096])).
% 1.64/1.83 tff(7100,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7101,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7100, 7099])).
% 1.64/1.83 tff(7102,plain,
% 1.64/1.83 (~b(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7101, 116, 7092, 6089, 7080, 7095])).
% 1.64/1.83 tff(7103,plain,
% 1.64/1.83 (r(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[808, 7102])).
% 1.64/1.83 tff(7104,plain,
% 1.64/1.83 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[568, 7084])).
% 1.64/1.83 tff(7105,plain,
% 1.64/1.83 (~(s(elem!1) = s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[842, 7084])).
% 1.64/1.83 tff(7106,plain,
% 1.64/1.83 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[529, 7084, 7068])).
% 1.64/1.83 tff(7107,plain,
% 1.64/1.83 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[836, 7084, 7106])).
% 1.64/1.83 tff(7108,plain,
% 1.64/1.83 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7085])).
% 1.64/1.83 tff(7109,plain,
% 1.64/1.83 (b(s(elem!1), z)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[6436, 7108])).
% 1.64/1.83 tff(7110,plain,
% 1.64/1.83 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[6919, 7109, 7074, 6980, 7107, 7105])).
% 1.64/1.83 tff(7111,plain,
% 1.64/1.83 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[885, 7110, 7104])).
% 1.64/1.83 tff(7112,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[6926, 7111, 7103, 6089, 7093, 7080, 7092])).
% 1.64/1.83 tff(7113,plain,(b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7114,plain,
% 1.64/1.83 (b(s(s(z)), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1303, 1676])).
% 1.64/1.83 tff(7115,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1, 7114])).
% 1.64/1.83 tff(7116,plain,((~(elem!1 = z)) | b(s(s(z)), elem!1) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7117,plain,
% 1.64/1.83 ((~(elem!1 = z)) | b(s(s(z)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7116, 7113])).
% 1.64/1.83 tff(7118,plain,
% 1.64/1.83 (~(elem!1 = z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7117, 1])).
% 1.64/1.83 tff(7119,plain,
% 1.64/1.83 (~(z = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[445, 7118])).
% 1.64/1.83 tff(7120,plain,
% 1.64/1.83 (r(s(s(z)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[6773, 4432])).
% 1.64/1.83 tff(7121,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[201, 77, 155, 67, 292])).
% 1.64/1.83 tff(7122,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7123,plain,
% 1.64/1.83 (~r(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7122, 64, 292])).
% 1.64/1.83 tff(7124,plain,
% 1.64/1.83 (b(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[210, 7123])).
% 1.64/1.83 tff(7125,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7126,plain,
% 1.64/1.83 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7127,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7126])).
% 1.64/1.83 tff(7128,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7127, 7125])).
% 1.64/1.83 tff(7129,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7130,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7129, 7128])).
% 1.64/1.83 tff(7131,plain,
% 1.64/1.83 (~b(s(z), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7130, 116, 7124, 271, 7113])).
% 1.64/1.83 tff(7132,plain,
% 1.64/1.83 (r(s(z), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[172, 7131])).
% 1.64/1.83 tff(7133,plain,
% 1.64/1.83 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[4107])).
% 1.64/1.83 tff(7134,plain,
% 1.64/1.83 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7133])).
% 1.64/1.83 tff(7135,plain,
% 1.64/1.83 (~(elem!1 = z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[409, 7124, 340])).
% 1.64/1.83 tff(7136,plain,
% 1.64/1.83 (~(z = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[445, 7135])).
% 1.64/1.83 tff(7137,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7138,plain,
% 1.64/1.83 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7139,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7138])).
% 1.64/1.83 tff(7140,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[7139, 7137])).
% 1.64/1.83 tff(7141,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(7142,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7141, 7140])).
% 1.64/1.83 tff(7143,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7142, 116, 271, 1303, 2329, 2321])).
% 1.64/1.83 tff(7144,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7145,plain,
% 1.64/1.83 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7144, 271, 7113, 292])).
% 1.64/1.83 tff(7146,plain,
% 1.64/1.83 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[105, 7145])).
% 1.64/1.83 tff(7147,plain,
% 1.64/1.83 (~b(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1298, 1055, 271, 7124])).
% 1.64/1.83 tff(7148,plain,
% 1.64/1.83 (~(elem!1 = s(s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[422, 7134])).
% 1.64/1.83 tff(7149,plain,
% 1.64/1.83 (~r(s(z), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4008, 428, 156])).
% 1.64/1.83 tff(7150,plain,
% 1.64/1.83 (s(z) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[357, 7149, 340])).
% 1.64/1.83 tff(7151,plain,
% 1.64/1.83 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7150])).
% 1.64/1.83 tff(7152,plain,
% 1.64/1.83 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.83 inference(transitivity,[status(thm)],[7151, 4222])).
% 1.64/1.83 tff(7153,plain,
% 1.64/1.83 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7152])).
% 1.64/1.83 tff(7154,plain,
% 1.64/1.83 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1901, 7153])).
% 1.64/1.83 tff(7155,plain,
% 1.64/1.83 (s(s(z)) = s(elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7150])).
% 1.64/1.83 tff(7156,plain,
% 1.64/1.83 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7155])).
% 1.64/1.83 tff(7157,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[7156])).
% 1.64/1.83 tff(7158,plain,
% 1.64/1.83 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7157])).
% 1.64/1.83 tff(7159,plain,
% 1.64/1.83 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[7158])).
% 1.64/1.83 tff(7160,plain,
% 1.64/1.83 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7155])).
% 1.64/1.83 tff(7161,plain,
% 1.64/1.83 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[27, 7160])).
% 1.64/1.83 tff(7162,plain,
% 1.64/1.83 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[7161, 7159])).
% 1.64/1.83 tff(7163,plain,
% 1.64/1.83 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7156])).
% 1.64/1.83 tff(7164,plain,
% 1.64/1.83 ((~b(s(s(s(z))), z)) <=> (~b(s(s(elem!1)), z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7163])).
% 1.64/1.83 tff(7165,plain,
% 1.64/1.83 (~b(s(s(elem!1)), z)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[57, 7164])).
% 1.64/1.83 tff(7166,plain,
% 1.64/1.83 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[2578])).
% 1.64/1.83 tff(7167,plain,
% 1.64/1.83 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.64/1.83 inference(symmetry,[status(thm)],[7166])).
% 1.64/1.83 tff(7168,plain,
% 1.64/1.83 (b(s(s(elem!1)), z)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1303, 7167])).
% 1.64/1.83 tff(7169,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2830, 7168])).
% 1.64/1.83 tff(7170,plain,((~(elem!1 = z)) | b(s(s(elem!1)), z) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(7171,plain,
% 1.64/1.83 (~(elem!1 = z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7170, 2830, 1303])).
% 1.64/1.83 tff(7172,plain,
% 1.64/1.83 (~(elem!1 = s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[420, 3468])).
% 1.64/1.83 tff(7173,plain,
% 1.64/1.83 (b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[743, 574, 1373])).
% 1.64/1.83 tff(7174,plain,
% 1.64/1.83 (~b(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3195, 7173, 1055, 270])).
% 1.64/1.83 tff(7175,plain,
% 1.64/1.83 (r(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[633, 7174, 1046])).
% 1.64/1.83 tff(7176,plain,
% 1.64/1.83 (~r(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2095, 7175, 575])).
% 1.64/1.83 tff(7177,plain,
% 1.64/1.83 (b(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[289, 7176])).
% 1.64/1.83 tff(7178,plain,
% 1.64/1.83 (~b(s(s(z)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2698, 116, 270, 7177, 1303])).
% 1.64/1.83 tff(7179,plain,
% 1.64/1.83 ((s(s(z)) = s(z)) | r(s(s(z)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[391, 21, 7178])).
% 1.64/1.83 tff(7180,plain,
% 1.64/1.83 (r(s(s(z)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[7179, 2692])).
% 1.64/1.83 tff(7181,plain,
% 1.64/1.83 (~r(s(s(z)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2707, 77, 575, 7175, 7180])).
% 1.64/1.83 tff(7182,plain,
% 1.64/1.83 (b(s(s(z)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[426, 7181, 422])).
% 1.64/1.83 tff(7183,plain,
% 1.64/1.83 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2182, 574])).
% 1.64/1.83 tff(7184,plain,
% 1.64/1.83 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2207, 7175, 1055, 270, 575])).
% 1.64/1.83 tff(7185,plain,
% 1.64/1.83 (b(elem!1, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1892, 7184, 7183])).
% 1.64/1.83 tff(7186,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7187,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(7188,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[7187])).
% 1.64/1.83 tff(7189,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7188, 7186])).
% 1.64/1.84 tff(7190,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7191,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7190, 7189])).
% 1.64/1.84 tff(7192,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7191, 116, 1055, 7173, 7185, 1303, 7182])).
% 1.64/1.84 tff(7193,plain,((s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1) | (~r(elem!1, z)) | (~b(s(z), z)) | (elem!1 = s(z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7194,plain,
% 1.64/1.84 (s(s(elem!1)) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7193, 3470, 1303, 422, 1055, 270, 7172, 1373])).
% 1.64/1.84 tff(7195,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7194])).
% 1.64/1.84 tff(7196,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.84 inference(transitivity,[status(thm)],[7195, 591])).
% 1.64/1.84 tff(7197,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7196, 1743])).
% 1.64/1.84 tff(7198,plain,
% 1.64/1.84 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7197])).
% 1.64/1.84 tff(7199,plain,
% 1.64/1.84 (elem!1 = s(s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1097, 7194])).
% 1.64/1.84 tff(7200,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(7201,plain,
% 1.64/1.84 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.84 inference(symmetry,[status(thm)],[7200])).
% 1.64/1.84 tff(7202,plain,
% 1.64/1.84 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7201])).
% 1.64/1.84 tff(7203,plain,
% 1.64/1.84 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[7202])).
% 1.64/1.84 tff(7204,plain,
% 1.64/1.84 (s(s(elem!1)) = elem!1),
% 1.64/1.84 inference(symmetry,[status(thm)],[1080])).
% 1.64/1.84 tff(7205,plain,
% 1.64/1.84 (s(s(s(elem!1))) = s(elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7204])).
% 1.64/1.84 tff(7206,plain,
% 1.64/1.84 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7201])).
% 1.64/1.84 tff(7207,plain,
% 1.64/1.84 (s(s(s(s(z)))) = s(s(z))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7206, 7205, 561, 7203, 38])).
% 1.64/1.84 tff(7208,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[141, 7207])).
% 1.64/1.84 tff(7209,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(s(z)))) = s(s(z))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7210,plain,
% 1.64/1.84 ((~(s(s(elem!1)) = s(s(s(z))))) | (~(elem!1 = s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7209, 137])).
% 1.64/1.84 tff(7211,plain,
% 1.64/1.84 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7210, 7199])).
% 1.64/1.84 tff(7212,plain,
% 1.64/1.84 (~(elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7211, 7198])).
% 1.64/1.84 tff(7213,plain,
% 1.64/1.84 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7196])).
% 1.64/1.84 tff(7214,plain,
% 1.64/1.84 (~(s(s(s(z))) = elem!1)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7211, 7213])).
% 1.64/1.84 tff(7215,plain,
% 1.64/1.84 (~r(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2769, 7214, 1055, 7212, 3470, 270, 1303, 422])).
% 1.64/1.84 tff(7216,plain,
% 1.64/1.84 (b(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[633, 7215, 7172])).
% 1.64/1.84 tff(7217,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7218,plain,
% 1.64/1.84 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7219,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7218])).
% 1.64/1.84 tff(7220,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7219, 7217])).
% 1.64/1.84 tff(7221,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7222,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7221, 7220])).
% 1.64/1.84 tff(7223,plain,
% 1.64/1.84 (~b(s(z), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7222, 116, 1055, 270, 7216, 1303])).
% 1.64/1.84 tff(7224,plain,
% 1.64/1.84 (r(s(z), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[170, 21, 54, 7223])).
% 1.64/1.84 tff(7225,plain,
% 1.64/1.84 (b(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[357, 353, 1700])).
% 1.64/1.84 tff(7226,plain,
% 1.64/1.84 (~b(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2085, 7225, 1055, 270])).
% 1.64/1.84 tff(7227,plain,
% 1.64/1.84 (r(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[633, 7226, 421])).
% 1.64/1.84 tff(7228,plain,
% 1.64/1.84 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2207, 7227, 1055, 270, 575])).
% 1.64/1.84 tff(7229,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.64/1.84 tff(7230,plain,
% 1.64/1.84 (b(elem!1, s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1892, 7183, 7229])).
% 1.64/1.84 tff(7231,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7232,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7233,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7232])).
% 1.64/1.84 tff(7234,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7233, 7231])).
% 1.64/1.84 tff(7235,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7236,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7235, 7234])).
% 1.64/1.84 tff(7237,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7236, 116, 1055, 616, 847, 270, 1879])).
% 1.64/1.84 tff(7238,plain,((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7239,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7238, 7230, 7173, 1055, 847, 270])).
% 1.64/1.84 tff(7240,plain,((s(s(elem!1)) = elem!1) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(elem!1, s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7241,plain,
% 1.64/1.84 (s(s(elem!1)) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7240, 7225, 1055, 270, 7228, 1373])).
% 1.64/1.84 tff(7242,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[521])).
% 1.64/1.84 tff(7243,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.84 inference(transitivity,[status(thm)],[7242, 591])).
% 1.64/1.84 tff(7244,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7243, 1743])).
% 1.64/1.84 tff(7245,plain,
% 1.64/1.84 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7244])).
% 1.64/1.84 tff(7246,plain,
% 1.64/1.84 (elem!1 = s(s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1097, 521])).
% 1.64/1.84 tff(7247,plain,
% 1.64/1.84 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7210, 7246])).
% 1.64/1.84 tff(7248,plain,
% 1.64/1.84 (~(elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7247, 7245])).
% 1.64/1.84 tff(7249,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.64/1.84 tff(7250,plain,
% 1.64/1.84 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[521])).
% 1.64/1.84 tff(7251,plain,
% 1.64/1.84 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(symmetry,[status(thm)],[7250])).
% 1.64/1.84 tff(7252,plain,
% 1.64/1.84 (b(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[667, 7251])).
% 1.64/1.84 tff(7253,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7249, 7252])).
% 1.64/1.84 tff(7254,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7255,plain,
% 1.64/1.84 (~b(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7254, 521, 7249])).
% 1.64/1.84 tff(7256,plain,
% 1.64/1.84 (r(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[633, 7255, 1046])).
% 1.64/1.84 tff(7257,plain,
% 1.64/1.84 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7243])).
% 1.64/1.84 tff(7258,plain,
% 1.64/1.84 (~(s(s(s(z))) = elem!1)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7247, 7257])).
% 1.64/1.84 tff(7259,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7260,plain,
% 1.64/1.84 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7261,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7260])).
% 1.64/1.84 tff(7262,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7261, 7259])).
% 1.64/1.84 tff(7263,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7264,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7263, 7262])).
% 1.64/1.84 tff(7265,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7264, 116, 847, 270, 2189, 2247])).
% 1.64/1.84 tff(7266,plain,
% 1.64/1.84 (r(s(s(s(z))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[402, 21, 135, 7265])).
% 1.64/1.84 tff(7267,plain,
% 1.64/1.84 (~r(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2750, 77, 620, 7266])).
% 1.64/1.84 tff(7268,plain,
% 1.64/1.84 (b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1345, 7267, 1620])).
% 1.64/1.84 tff(7269,plain,
% 1.64/1.84 (~r(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2758, 77, 575, 620, 7266])).
% 1.64/1.84 tff(7270,plain,
% 1.64/1.84 (b(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2725, 7269, 2688])).
% 1.64/1.84 tff(7271,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2767, 7270, 7268, 1055, 2247])).
% 1.64/1.84 tff(7272,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7273,plain,
% 1.64/1.84 (~b(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7272, 7258, 1055, 7248, 575, 7256, 847, 270])).
% 1.64/1.84 tff(7274,plain,
% 1.64/1.84 (r(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[63, 7273])).
% 1.64/1.84 tff(7275,plain,
% 1.64/1.84 (~r(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2162, 77, 575, 7274])).
% 1.64/1.84 tff(7276,plain,
% 1.64/1.84 (b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1345, 7275, 7248])).
% 1.64/1.84 tff(7277,plain,
% 1.64/1.84 (~r(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2717, 77, 575, 7274])).
% 1.64/1.84 tff(7278,plain,
% 1.64/1.84 (b(s(s(s(z))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2725, 7277, 7258])).
% 1.64/1.84 tff(7279,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7280,plain,
% 1.64/1.84 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7281,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7280])).
% 1.64/1.84 tff(7282,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7281, 7279])).
% 1.64/1.84 tff(7283,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7284,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7283, 7282])).
% 1.64/1.84 tff(7285,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7284, 116, 1055, 847, 270, 7278, 7276])).
% 1.64/1.84 tff(7286,plain,((~(s(s(elem!1)) = elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~r(elem!1, z)) | (elem!1 = s(z)) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7287,plain,
% 1.64/1.84 (b(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7286, 7241, 7225, 270, 575, 421, 1055])).
% 1.64/1.84 tff(7288,plain,
% 1.64/1.84 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7251])).
% 1.64/1.84 tff(7289,plain,
% 1.64/1.84 (~b(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[6228, 7288])).
% 1.64/1.84 tff(7290,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1436, 7289])).
% 1.64/1.84 tff(7291,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(elem!1)), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7292,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7291, 7287, 7241, 7226])).
% 1.64/1.84 tff(7293,plain,((s(z) = elem!1) | (~b(s(z), z)) | (~r(elem!1, z)) | (~b(z, elem!1)) | r(s(s(elem!1)), elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7294,plain,
% 1.64/1.84 (r(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7293, 3468, 3470, 1055, 1373, 270])).
% 1.64/1.84 tff(7295,plain,
% 1.64/1.84 (~r(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4008, 7294, 7224])).
% 1.64/1.84 tff(7296,plain,
% 1.64/1.84 (b(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[426, 7295, 422])).
% 1.64/1.84 tff(7297,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2822, 116, 1055, 270, 7216, 1303, 7296])).
% 1.64/1.84 tff(7298,plain,(b(elem!1, z) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1) | r(s(s(elem!1)), elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7299,plain,
% 1.64/1.84 (b(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7298, 1373, 270, 1303, 422, 1055, 7171])).
% 1.64/1.84 tff(7300,plain,
% 1.64/1.84 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[521])).
% 1.64/1.84 tff(7301,plain,
% 1.64/1.84 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.64/1.84 inference(symmetry,[status(thm)],[7300])).
% 1.64/1.84 tff(7302,plain,
% 1.64/1.84 (b(s(s(elem!1)), z)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[537, 7301])).
% 1.64/1.84 tff(7303,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2830, 7302])).
% 1.64/1.84 tff(7304,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(7305,plain,
% 1.64/1.84 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7304, 7299, 2830])).
% 1.64/1.84 tff(7306,plain,
% 1.64/1.84 (b(s(s(elem!1)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[743, 7305, 1373])).
% 1.64/1.84 tff(7307,plain,
% 1.64/1.84 (r(s(s(elem!1)), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3219, 2830])).
% 1.64/1.84 tff(7308,plain,
% 1.64/1.84 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7309,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[7308])).
% 1.64/1.84 tff(7310,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[7309, 2108])).
% 1.64/1.84 tff(7311,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(7312,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[7311, 7310])).
% 1.64/1.84 tff(7313,plain,
% 1.64/1.84 (~b(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[7312, 116, 1055, 7299, 270])).
% 1.64/1.84 tff(7314,plain,
% 1.64/1.84 (~b(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2658, 116, 1055, 7299, 1303])).
% 1.64/1.84 tff(7315,plain,
% 1.64/1.84 (r(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[426, 7314, 422])).
% 1.64/1.84 tff(7316,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(7317,plain,
% 1.64/1.84 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7318,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7317])).
% 1.64/1.85 tff(7319,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7318, 7316])).
% 1.64/1.85 tff(7320,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(7321,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7320, 7319])).
% 1.64/1.85 tff(7322,plain,
% 1.64/1.85 (~b(s(z), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7321, 116, 1055, 7299, 270, 1303])).
% 1.64/1.85 tff(7323,plain,
% 1.64/1.85 (r(s(z), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[170, 21, 54, 7322])).
% 1.64/1.85 tff(7324,plain,
% 1.64/1.85 (~r(s(z), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4008, 7323, 7315])).
% 1.64/1.85 tff(7325,plain,
% 1.64/1.85 (s(z) = elem!1),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[357, 7324, 7313])).
% 1.64/1.85 tff(7326,plain,
% 1.64/1.85 (s(s(z)) = s(elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7325])).
% 1.64/1.85 tff(7327,plain,
% 1.64/1.85 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7326])).
% 1.64/1.85 tff(7328,plain,
% 1.64/1.85 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7327])).
% 1.64/1.85 tff(7329,plain,
% 1.64/1.85 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7328, 1504])).
% 1.64/1.85 tff(7330,plain,
% 1.64/1.85 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7329])).
% 1.64/1.85 tff(7331,plain,
% 1.64/1.85 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1138, 7330])).
% 1.64/1.85 tff(7332,plain,
% 1.64/1.85 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4310, 7331, 7307, 1055, 7299, 7306])).
% 1.64/1.85 tff(7333,plain,
% 1.64/1.85 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7326])).
% 1.64/1.85 tff(7334,plain,
% 1.64/1.85 (r(s(elem!1), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7315, 7333])).
% 1.64/1.85 tff(7335,plain,
% 1.64/1.85 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1531, 7325])).
% 1.64/1.85 tff(7336,plain,
% 1.64/1.85 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1584, 7335])).
% 1.64/1.85 tff(7337,plain,
% 1.64/1.85 (~b(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4370, 7325, 7307, 1055, 7299, 7306])).
% 1.64/1.85 tff(7338,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1596, 7337, 7336])).
% 1.64/1.85 tff(7339,plain,
% 1.64/1.85 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7326])).
% 1.64/1.85 tff(7340,plain,
% 1.64/1.85 (b(s(elem!1), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1303, 7339])).
% 1.64/1.85 tff(7341,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7326])).
% 1.64/1.85 tff(7342,plain,
% 1.64/1.85 (s(elem!1) = s(s(z))),
% 1.64/1.85 inference(symmetry,[status(thm)],[7326])).
% 1.64/1.85 tff(7343,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7342])).
% 1.64/1.85 tff(7344,plain,
% 1.64/1.85 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7343])).
% 1.64/1.85 tff(7345,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7346,plain,
% 1.64/1.85 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7347,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7346])).
% 1.64/1.85 tff(7348,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7347, 7345])).
% 1.64/1.85 tff(7349,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(7350,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7349, 7348])).
% 1.64/1.85 tff(7351,plain,
% 1.64/1.85 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7350, 77, 7338, 7334])).
% 1.64/1.85 tff(7352,plain,
% 1.64/1.85 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7351, 7344])).
% 1.64/1.85 tff(7353,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[226, 7352])).
% 1.64/1.85 tff(7354,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7353, 7341])).
% 1.64/1.85 tff(7355,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.64/1.85 tff(7356,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7357,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(7358,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7357, 7356])).
% 1.64/1.85 tff(7359,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7358, 116, 1055, 537, 7355, 2844, 254])).
% 1.64/1.85 tff(7360,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(7361,plain,
% 1.64/1.85 (~b(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7360, 7299, 1055, 7354, 7340])).
% 1.64/1.85 tff(7362,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[247, 7361])).
% 1.64/1.85 tff(7363,plain,
% 1.64/1.85 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1393])).
% 1.64/1.85 tff(7364,plain,
% 1.64/1.85 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4342, 7325])).
% 1.64/1.85 tff(7365,plain,
% 1.64/1.85 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1707, 7364])).
% 1.64/1.85 tff(7366,plain,
% 1.64/1.85 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7365, 7363])).
% 1.64/1.85 tff(7367,plain,
% 1.64/1.85 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1364, 7335])).
% 1.64/1.85 tff(7368,plain,
% 1.64/1.85 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7326])).
% 1.64/1.85 tff(7369,plain,
% 1.64/1.85 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7342])).
% 1.64/1.85 tff(7370,plain,
% 1.64/1.85 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7369])).
% 1.64/1.85 tff(7371,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7372,plain,
% 1.64/1.85 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7373,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7372])).
% 1.64/1.85 tff(7374,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7373, 7371])).
% 1.64/1.85 tff(7375,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(7376,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7375, 7374])).
% 1.64/1.85 tff(7377,plain,
% 1.64/1.85 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7376, 77, 7338, 7334])).
% 1.64/1.85 tff(7378,plain,
% 1.64/1.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7377, 7370])).
% 1.64/1.85 tff(7379,plain,
% 1.64/1.85 (b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[149, 7378])).
% 1.64/1.85 tff(7380,plain,
% 1.64/1.85 (b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7379, 7368])).
% 1.64/1.85 tff(7381,plain,
% 1.64/1.85 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5045, 77, 1027, 650])).
% 1.64/1.85 tff(7382,plain,
% 1.64/1.85 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[858, 21, 855, 7381])).
% 1.64/1.85 tff(7383,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7384,plain,
% 1.64/1.85 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7385,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7384])).
% 1.64/1.85 tff(7386,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7385, 7383])).
% 1.64/1.85 tff(7387,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(7388,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7387, 7386])).
% 1.64/1.85 tff(7389,plain,
% 1.64/1.85 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7388, 77, 228, 2418, 1027])).
% 1.64/1.85 tff(7390,plain,
% 1.64/1.85 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1405, 7389, 6021])).
% 1.64/1.85 tff(7391,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.85 tff(7392,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7393,plain,
% 1.64/1.85 (((~b(s(elem!1), s(s(s(s(z)))))) | (~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(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7394,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7393])).
% 1.64/1.85 tff(7395,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7394, 7392])).
% 1.64/1.85 tff(7396,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(7397,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7396, 7395])).
% 1.64/1.85 tff(7398,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7397, 116, 7355, 7391, 7390, 7382])).
% 1.64/1.85 tff(7399,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(7400,plain,
% 1.64/1.85 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7399, 7354, 7380, 7367, 7366, 7362, 7338, 7334])).
% 1.64/1.85 tff(7401,plain,
% 1.64/1.85 (s(s(s(s(s(z))))) = elem!1),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[885, 7400, 7332])).
% 1.64/1.85 tff(7402,plain,
% 1.64/1.85 (elem!1 = s(s(s(s(s(z)))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[7401])).
% 1.64/1.85 tff(7403,plain,
% 1.64/1.85 (s(z) = s(s(s(s(s(z)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7325, 7402])).
% 1.64/1.85 tff(7404,plain,
% 1.64/1.85 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7403])).
% 1.64/1.85 tff(7405,plain,
% 1.64/1.85 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.64/1.85 inference(symmetry,[status(thm)],[7404])).
% 1.64/1.85 tff(7406,plain,
% 1.64/1.85 (s(s(s(s(z)))) = z),
% 1.64/1.85 inference(transitivity,[status(thm)],[554, 7405, 47])).
% 1.64/1.85 tff(7407,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[242, 7406])).
% 1.64/1.85 tff(7408,plain,(r(s(s(elem!1)), elem!1) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (s(s(z)) = elem!1) | (~b(s(z), z)) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(7409,plain,
% 1.64/1.85 (r(s(s(elem!1)), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7408, 7165, 7113, 270, 1055, 422])).
% 1.64/1.85 tff(7410,plain,
% 1.64/1.85 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7155])).
% 1.64/1.85 tff(7411,plain,
% 1.64/1.85 (r(s(elem!1), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[428, 7410])).
% 1.64/1.85 tff(7412,plain,
% 1.64/1.85 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1531, 7150])).
% 1.64/1.85 tff(7413,plain,
% 1.64/1.85 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1364, 7412])).
% 1.64/1.85 tff(7414,plain,
% 1.64/1.85 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7156])).
% 1.64/1.85 tff(7415,plain,
% 1.64/1.85 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7414, 1504])).
% 1.64/1.85 tff(7416,plain,
% 1.64/1.85 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7415])).
% 1.64/1.85 tff(7417,plain,
% 1.64/1.85 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1138, 7416])).
% 1.64/1.85 tff(7418,plain,
% 1.64/1.85 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7155])).
% 1.64/1.85 tff(7419,plain,
% 1.64/1.85 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7418, 1820])).
% 1.64/1.85 tff(7420,plain,
% 1.64/1.85 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7419])).
% 1.64/1.85 tff(7421,plain,
% 1.64/1.85 (~(elem!1 = z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[409, 270, 340])).
% 1.64/1.85 tff(7422,plain,
% 1.64/1.85 (~(z = elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[445, 7421])).
% 1.64/1.85 tff(7423,plain,
% 1.64/1.85 (~(s(s(z)) = s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5269, 7422])).
% 1.64/1.85 tff(7424,plain,
% 1.64/1.85 (~(s(s(elem!1)) = s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7423, 7420])).
% 1.64/1.85 tff(7425,plain,
% 1.64/1.85 (~r(s(s(elem!1)), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2865, 7409, 7150, 428])).
% 1.64/1.85 tff(7426,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[767, 7425, 7424])).
% 1.64/1.85 tff(7427,plain,
% 1.64/1.85 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4838, 7426, 7417, 7413, 7411, 7409, 7162])).
% 1.64/1.85 tff(7428,plain,
% 1.64/1.85 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[885, 7427, 7154])).
% 1.64/1.85 tff(7429,plain,
% 1.64/1.85 (b(elem!1, z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1458, 7150, 270])).
% 1.64/1.85 tff(7430,plain,
% 1.64/1.85 (~b(s(s(s(s(s(z))))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4300, 116, 1055, 7429, 7428])).
% 1.64/1.85 tff(7431,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[898, 21, 895, 7430])).
% 1.64/1.85 tff(7432,plain,
% 1.64/1.85 (r(s(s(elem!1)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1482, 7150, 64])).
% 1.64/1.85 tff(7433,plain,
% 1.64/1.85 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4308, 77, 7432, 7431])).
% 1.64/1.85 tff(7434,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[916, 21, 7417, 7433])).
% 1.64/1.85 tff(7435,plain,
% 1.64/1.85 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7156])).
% 1.64/1.85 tff(7436,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7157])).
% 1.64/1.85 tff(7437,plain,
% 1.64/1.85 ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7436])).
% 1.64/1.85 tff(7438,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7439,plain,
% 1.64/1.85 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7440,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7439])).
% 1.64/1.85 tff(7441,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[7440, 7438])).
% 1.64/1.85 tff(7442,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(7443,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7442, 7441])).
% 1.64/1.85 tff(7444,plain,
% 1.64/1.85 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[7443, 77, 7409, 7432, 7431])).
% 1.64/1.85 tff(7445,plain,
% 1.64/1.85 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7444, 7437])).
% 1.64/1.85 tff(7446,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)],[1380, 7445])).
% 1.64/1.85 tff(7447,plain,
% 1.64/1.85 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[7446, 7435])).
% 1.64/1.85 tff(7448,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7449,plain,
% 1.64/1.85 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(7450,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[7449])).
% 1.64/1.85 tff(7451,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[7450, 7448])).
% 1.64/1.86 tff(7452,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(7453,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7452, 7451])).
% 1.64/1.86 tff(7454,plain,
% 1.64/1.86 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7453, 116, 7162, 7428, 7447, 7434])).
% 1.64/1.86 tff(7455,plain,
% 1.64/1.86 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[858, 21, 7413, 7454])).
% 1.64/1.86 tff(7456,plain,
% 1.64/1.86 (s(elem!1) = s(s(z))),
% 1.64/1.86 inference(symmetry,[status(thm)],[7155])).
% 1.64/1.86 tff(7457,plain,
% 1.64/1.86 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7456])).
% 1.64/1.86 tff(7458,plain,
% 1.64/1.86 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[7457])).
% 1.64/1.86 tff(7459,plain,
% 1.64/1.86 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7155])).
% 1.64/1.86 tff(7460,plain,
% 1.64/1.86 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[7459])).
% 1.64/1.86 tff(7461,plain,
% 1.64/1.86 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7460])).
% 1.64/1.86 tff(7462,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2016, 7150, 28])).
% 1.64/1.86 tff(7463,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7464,plain,
% 1.64/1.86 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7465,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7464])).
% 1.64/1.86 tff(7466,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[7465, 7463])).
% 1.64/1.86 tff(7467,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(7468,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7467, 7466])).
% 1.64/1.86 tff(7469,plain,
% 1.64/1.86 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7468, 116, 7162, 7426, 7462])).
% 1.64/1.86 tff(7470,plain,
% 1.64/1.86 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7469, 7461])).
% 1.64/1.86 tff(7471,plain,
% 1.64/1.86 (r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[149, 7470])).
% 1.64/1.86 tff(7472,plain,
% 1.64/1.86 (r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7471, 7458])).
% 1.64/1.86 tff(7473,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7474,plain,
% 1.64/1.86 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7475,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7474])).
% 1.64/1.86 tff(7476,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[7475, 7473])).
% 1.64/1.86 tff(7477,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(7478,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7477, 7476])).
% 1.64/1.86 tff(7479,plain,
% 1.64/1.86 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7478, 116, 7462, 7428, 7447, 7434])).
% 1.64/1.86 tff(7480,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6694, 7479])).
% 1.64/1.86 tff(7481,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7482,plain,
% 1.64/1.86 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7483,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7482])).
% 1.64/1.86 tff(7484,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[7483, 7481])).
% 1.64/1.86 tff(7485,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), 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))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(7486,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7485, 7484])).
% 1.64/1.86 tff(7487,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7486, 77, 7480, 7472, 7455])).
% 1.64/1.86 tff(7488,plain,((~r(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (s(s(z)) = elem!1) | b(s(s(s(z))), z) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), elem!1) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(7489,plain,
% 1.64/1.86 (~r(s(s(z)), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7488, 422, 270, 1055, 57, 27, 28, 340, 156])).
% 1.64/1.86 tff(7490,plain,
% 1.64/1.86 (b(s(s(z)), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[426, 7489, 422])).
% 1.64/1.86 tff(7491,plain,
% 1.64/1.86 (~(s(z) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4434, 7490, 4432])).
% 1.64/1.86 tff(7492,plain,
% 1.64/1.86 (~(elem!1 = s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[420, 7491])).
% 1.64/1.86 tff(7493,plain,
% 1.64/1.86 (r(elem!1, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[633, 7492, 6228])).
% 1.64/1.86 tff(7494,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7495,plain,
% 1.64/1.86 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7496,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7495])).
% 1.64/1.86 tff(7497,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[7496, 7494])).
% 1.64/1.86 tff(7498,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(7499,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7498, 7497])).
% 1.64/1.86 tff(7500,plain,
% 1.64/1.86 (~r(elem!1, s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7499, 77, 7493, 7120])).
% 1.64/1.86 tff(7501,plain,
% 1.64/1.86 (b(elem!1, s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[6497, 7500, 7148])).
% 1.64/1.86 tff(7502,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7503,plain,
% 1.64/1.86 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7504,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7503])).
% 1.64/1.86 tff(7505,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[7504, 7502])).
% 1.64/1.86 tff(7506,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(7507,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7506, 7505])).
% 1.64/1.86 tff(7508,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7507, 116, 1055, 7113, 7490, 7501])).
% 1.64/1.86 tff(7509,plain,((s(s(z)) = elem!1) | (~b(z, elem!1)) | b(elem!1, s(z)) | b(s(s(z)), s(z)) | (~b(s(z), z)) | b(s(s(s(z))), z) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), elem!1) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(7510,plain,
% 1.64/1.86 (s(s(z)) = elem!1),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7509, 1055, 7147, 4432, 7124, 57, 7146, 28, 340, 7132])).
% 1.64/1.86 tff(7511,plain,
% 1.64/1.86 (s(s(s(z))) = s(elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7510])).
% 1.64/1.86 tff(7512,plain,
% 1.64/1.86 (s(elem!1) = s(s(s(z)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[7511])).
% 1.64/1.86 tff(7513,plain,
% 1.64/1.86 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7512])).
% 1.64/1.86 tff(7514,plain,
% 1.64/1.86 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.64/1.86 inference(symmetry,[status(thm)],[7513])).
% 1.64/1.86 tff(7515,plain,
% 1.64/1.86 (~(s(z) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[480, 7510])).
% 1.64/1.86 tff(7516,plain,
% 1.64/1.86 (r(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[357, 7515, 340])).
% 1.64/1.86 tff(7517,plain,
% 1.64/1.86 (~r(elem!1, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[368, 7516, 292])).
% 1.64/1.86 tff(7518,plain,
% 1.64/1.86 (b(elem!1, z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2403, 7510, 7113])).
% 1.64/1.86 tff(7519,plain,
% 1.64/1.86 (~(elem!1 = s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1470, 7518, 57])).
% 1.64/1.86 tff(7520,plain,
% 1.64/1.86 (b(elem!1, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1345, 7519, 7517])).
% 1.64/1.86 tff(7521,plain,
% 1.64/1.86 (b(elem!1, s(elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7520, 7514])).
% 1.64/1.86 tff(7522,plain,
% 1.64/1.86 (b(s(s(elem!1)), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3257, 7510, 28])).
% 1.64/1.86 tff(7523,plain,
% 1.64/1.86 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[608, 7510])).
% 1.64/1.86 tff(7524,plain,
% 1.64/1.86 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7511])).
% 1.64/1.86 tff(7525,plain,
% 1.64/1.86 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[7524])).
% 1.64/1.86 tff(7526,plain,
% 1.64/1.86 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7525])).
% 1.64/1.86 tff(7527,plain,
% 1.64/1.86 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7511])).
% 1.64/1.86 tff(7528,plain,
% 1.64/1.86 (r(s(elem!1), z)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[64, 7527])).
% 1.64/1.86 tff(7529,plain,
% 1.64/1.86 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[529, 7510, 7136])).
% 1.64/1.86 tff(7530,plain,
% 1.64/1.86 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[836, 7510, 7529])).
% 1.64/1.86 tff(7531,plain,
% 1.64/1.86 (b(s(s(elem!1)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[808, 1416])).
% 1.64/1.86 tff(7532,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.86 tff(7533,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4137, 77, 752, 360, 7532])).
% 1.64/1.86 tff(7534,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(7535,plain,
% 1.64/1.86 (~r(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7534, 752, 360])).
% 1.64/1.86 tff(7536,plain,
% 1.64/1.86 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[716, 21, 7535])).
% 1.64/1.86 tff(7537,plain,
% 1.64/1.86 (b(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7536, 706])).
% 1.64/1.86 tff(7538,plain,
% 1.64/1.86 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4610, 7537, 370, 7531, 752, 360])).
% 1.64/1.86 tff(7539,plain,
% 1.64/1.86 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[885, 7538, 569])).
% 1.64/1.86 tff(7540,plain,
% 1.64/1.86 (b(elem!1, z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2403, 370, 7113])).
% 1.64/1.86 tff(7541,plain,
% 1.64/1.86 (~b(s(s(s(s(s(z))))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4300, 116, 1055, 7540, 7539])).
% 1.64/1.86 tff(7542,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[898, 21, 895, 7541])).
% 1.64/1.86 tff(7543,plain,
% 1.64/1.86 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4643, 77, 5326, 7542])).
% 1.64/1.86 tff(7544,plain,
% 1.64/1.86 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[858, 21, 855, 7543])).
% 1.64/1.86 tff(7545,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7546,plain,
% 1.64/1.86 (((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(7547,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[7546])).
% 1.64/1.86 tff(7548,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[7547, 7545])).
% 1.64/1.86 tff(7549,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(7550,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[7549, 7548])).
% 1.64/1.86 tff(7551,plain,
% 1.64/1.86 (~b(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[7550, 116, 1055, 7531, 270, 271])).
% 1.64/1.86 tff(7552,plain,
% 1.64/1.86 (r(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3219, 7551])).
% 1.64/1.86 tff(7553,plain,
% 1.64/1.86 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4308, 77, 7552, 7542])).
% 1.64/1.86 tff(7554,plain,
% 1.64/1.86 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[916, 21, 913, 7553])).
% 1.64/1.87 tff(7555,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[555])).
% 1.64/1.87 tff(7556,plain,
% 1.64/1.87 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.87 inference(symmetry,[status(thm)],[7555])).
% 1.64/1.87 tff(7557,plain,
% 1.64/1.87 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7556])).
% 1.64/1.87 tff(7558,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7559,plain,
% 1.64/1.87 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7560,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7559])).
% 1.64/1.87 tff(7561,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[7560, 7558])).
% 1.64/1.87 tff(7562,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(7563,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7562, 7561])).
% 1.64/1.87 tff(7564,plain,
% 1.64/1.87 (~r(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7563, 77, 7552, 5326])).
% 1.64/1.87 tff(7565,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7564, 7557])).
% 1.64/1.87 tff(7566,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[664, 7565, 609])).
% 1.64/1.87 tff(7567,plain,
% 1.64/1.87 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4150, 7566, 370])).
% 1.64/1.87 tff(7568,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7569,plain,
% 1.64/1.87 (((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7570,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7569])).
% 1.64/1.87 tff(7571,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[7570, 7568])).
% 1.64/1.87 tff(7572,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(7573,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7572, 7571])).
% 1.64/1.87 tff(7574,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7573, 116, 7540, 7567, 7539, 7554, 7544])).
% 1.64/1.87 tff(7575,plain,((~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~(s(s(z)) = elem!1)) | (~b(z, elem!1)) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(7576,plain,
% 1.64/1.87 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7575, 7530, 7528, 7510, 1055, 7516, 7124, 271])).
% 1.64/1.87 tff(7577,plain,
% 1.64/1.87 (b(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[743, 7576, 7529])).
% 1.64/1.87 tff(7578,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7579,plain,
% 1.64/1.87 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7580,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7579])).
% 1.64/1.87 tff(7581,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[7580, 7578])).
% 1.64/1.87 tff(7582,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(7583,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7582, 7581])).
% 1.64/1.87 tff(7584,plain,
% 1.64/1.87 (~b(s(s(elem!1)), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7583, 116, 1055, 7518, 7577])).
% 1.64/1.87 tff(7585,plain,
% 1.64/1.87 (r(s(s(elem!1)), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3219, 7584])).
% 1.64/1.87 tff(7586,plain,
% 1.64/1.87 (~r(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7563, 77, 7585, 7528])).
% 1.64/1.87 tff(7587,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7586, 7526])).
% 1.64/1.87 tff(7588,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[664, 7587, 7523])).
% 1.64/1.87 tff(7589,plain,
% 1.64/1.87 (b(s(elem!1), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4150, 7588, 7510])).
% 1.64/1.87 tff(7590,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7591,plain,
% 1.64/1.87 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7592,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7591])).
% 1.64/1.87 tff(7593,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[7592, 7590])).
% 1.64/1.87 tff(7594,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(7595,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7594, 7593])).
% 1.64/1.87 tff(7596,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7595, 116, 7577, 7589, 7522, 7521])).
% 1.64/1.87 tff(7597,plain,((~b(z, elem!1)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | b(s(s(s(z))), z) | b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(7598,plain,
% 1.64/1.87 (~b(z, elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7597, 28, 292, 57, 340, 271, 4432])).
% 1.64/1.87 tff(7599,plain,
% 1.64/1.87 (r(z, elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1044, 7598, 7136])).
% 1.64/1.87 tff(7600,plain,
% 1.64/1.87 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4792])).
% 1.64/1.87 tff(7601,plain,
% 1.64/1.87 (~b(z, s(z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2217, 7600])).
% 1.64/1.87 tff(7602,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[271, 7601])).
% 1.64/1.87 tff(7603,plain,((~(s(z) = elem!1)) | (~b(z, s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(7604,plain,
% 1.64/1.87 (~(s(z) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7603, 7598, 271])).
% 1.64/1.87 tff(7605,plain,
% 1.64/1.87 (r(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[357, 7604, 340])).
% 1.64/1.87 tff(7606,plain,
% 1.64/1.87 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1446, 7605, 7599, 7124])).
% 1.64/1.87 tff(7607,plain,
% 1.64/1.87 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[636])).
% 1.64/1.87 tff(7608,plain,
% 1.64/1.87 (r(z, s(s(z))) <=> r(z, elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[370])).
% 1.64/1.87 tff(7609,plain,
% 1.64/1.87 (r(z, elem!1) <=> r(z, s(s(z)))),
% 1.64/1.87 inference(symmetry,[status(thm)],[7608])).
% 1.64/1.87 tff(7610,plain,
% 1.64/1.87 (r(z, s(s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[448, 7609])).
% 1.64/1.87 tff(7611,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7612,plain,
% 1.64/1.87 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7613,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7612])).
% 1.64/1.87 tff(7614,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[7613, 7611])).
% 1.64/1.87 tff(7615,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(7616,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7615, 7614])).
% 1.64/1.87 tff(7617,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7616, 77, 67, 1212, 65])).
% 1.64/1.87 tff(7618,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(7619,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7618, 7610, 67])).
% 1.64/1.87 tff(7620,plain,
% 1.64/1.87 (~r(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7619, 7607])).
% 1.64/1.87 tff(7621,plain,
% 1.64/1.87 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[593])).
% 1.64/1.87 tff(7622,plain,
% 1.64/1.87 (~(s(s(s(z))) = elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[100, 7621])).
% 1.64/1.87 tff(7623,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[370])).
% 1.64/1.87 tff(7624,plain,
% 1.64/1.87 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7623])).
% 1.64/1.87 tff(7625,plain,
% 1.64/1.87 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[529, 370, 518])).
% 1.64/1.87 tff(7626,plain,
% 1.64/1.87 (b(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[743, 7625, 1373])).
% 1.64/1.87 tff(7627,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[556, 370])).
% 1.64/1.87 tff(7628,plain,
% 1.64/1.87 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.87 inference(symmetry,[status(thm)],[7627])).
% 1.64/1.87 tff(7629,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[616, 7628])).
% 1.64/1.87 tff(7630,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.64/1.87 tff(7631,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7630, 7629])).
% 1.64/1.87 tff(7632,plain,((~(s(s(z)) = elem!1)) | b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(7633,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7632, 7626, 370])).
% 1.64/1.87 tff(7634,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[220, 7633, 27, 28])).
% 1.64/1.87 tff(7635,plain,
% 1.64/1.87 (~b(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7634, 7624])).
% 1.64/1.87 tff(7636,plain,
% 1.64/1.87 (r(s(s(s(z))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2725, 7635, 7622])).
% 1.64/1.87 tff(7637,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7636, 7620])).
% 1.64/1.87 tff(7638,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(elem!1)), elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(7639,plain,
% 1.64/1.87 (~(s(s(z)) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7638, 7599, 64, 7146, 28, 7606, 7136])).
% 1.64/1.87 tff(7640,plain,
% 1.64/1.87 (~(elem!1 = s(s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7639, 7134])).
% 1.64/1.87 tff(7641,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[870, 21, 1901, 4582])).
% 1.64/1.87 tff(7642,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7643,plain,
% 1.64/1.87 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7644,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7643])).
% 1.64/1.87 tff(7645,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[7644, 7642])).
% 1.64/1.87 tff(7646,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(7647,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[7646, 7645])).
% 1.64/1.87 tff(7648,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7647, 116, 270, 271, 1031, 7641])).
% 1.64/1.87 tff(7649,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(7650,plain,
% 1.64/1.87 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[7649, 7599, 271, 7124, 7605])).
% 1.64/1.87 tff(7651,plain,
% 1.64/1.87 (~r(elem!1, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[368, 7605, 292])).
% 1.64/1.87 tff(7652,plain,
% 1.64/1.87 (~r(s(s(z)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4008, 7605, 7132])).
% 1.64/1.87 tff(7653,plain,
% 1.64/1.87 (b(s(s(z)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[426, 7639, 7652])).
% 1.64/1.87 tff(7654,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7655,plain,
% 1.64/1.87 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(7656,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[7655])).
% 1.64/1.87 tff(7657,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[7656, 7654])).
% 1.64/1.87 tff(7658,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(7659,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7658, 7657])).
% 1.64/1.88 tff(7660,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7659, 116, 537, 270, 271, 7113, 1331])).
% 1.64/1.88 tff(7661,plain,((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(7662,plain,
% 1.64/1.88 (~b(elem!1, z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7661, 7653, 271, 7124])).
% 1.64/1.88 tff(7663,plain,
% 1.64/1.88 (r(elem!1, z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[545, 7662, 7135])).
% 1.64/1.88 tff(7664,plain,
% 1.64/1.88 (~r(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2717, 77, 7663, 64])).
% 1.64/1.88 tff(7665,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[547])).
% 1.64/1.88 tff(7666,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.88 inference(transitivity,[status(thm)],[7665, 591])).
% 1.64/1.88 tff(7667,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[7666, 1743])).
% 1.64/1.88 tff(7668,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7667])).
% 1.64/1.88 tff(7669,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1138, 7668])).
% 1.64/1.88 tff(7670,plain,
% 1.64/1.88 (b(elem!1, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1345, 7669, 4094])).
% 1.64/1.88 tff(7671,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7666])).
% 1.64/1.88 tff(7672,plain,
% 1.64/1.88 (~(s(s(s(z))) = elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1138, 7671])).
% 1.64/1.88 tff(7673,plain,
% 1.64/1.88 (b(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2725, 7672, 2719])).
% 1.64/1.88 tff(7674,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7675,plain,
% 1.64/1.88 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~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)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7676,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7675])).
% 1.64/1.88 tff(7677,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[7676, 7674])).
% 1.64/1.88 tff(7678,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7679,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7678, 7677])).
% 1.64/1.88 tff(7680,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7679, 116, 7673, 7670, 27, 1331])).
% 1.64/1.88 tff(7681,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(7682,plain,
% 1.64/1.88 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7681, 7664, 7653, 7651, 7146])).
% 1.64/1.88 tff(7683,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[885, 7682, 7650])).
% 1.64/1.88 tff(7684,plain,
% 1.64/1.88 (~(s(s(z)) = s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5269, 7136])).
% 1.64/1.88 tff(7685,plain,
% 1.64/1.88 ((~b(elem!1, z)) <=> (~b(s(s(elem!1)), z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7301])).
% 1.64/1.88 tff(7686,plain,
% 1.64/1.88 (~b(s(s(elem!1)), z)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1455, 7685])).
% 1.64/1.88 tff(7687,plain,
% 1.64/1.88 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7204])).
% 1.64/1.88 tff(7688,plain,
% 1.64/1.88 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[7687])).
% 1.64/1.88 tff(7689,plain,
% 1.64/1.88 (b(s(s(z)), s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1331, 7688])).
% 1.64/1.88 tff(7690,plain,
% 1.64/1.88 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[587])).
% 1.64/1.88 tff(7691,plain,
% 1.64/1.88 ((~(s(s(elem!1)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7690])).
% 1.64/1.88 tff(7692,assumption,(~(s(s(elem!1)) = s(s(s(z))))), introduced(assumption)).
% 1.64/1.88 tff(7693,plain,
% 1.64/1.88 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7692, 7691])).
% 1.64/1.88 tff(7694,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7695,plain,
% 1.64/1.88 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7696,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7695])).
% 1.64/1.88 tff(7697,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[7696, 7694])).
% 1.64/1.88 tff(7698,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7699,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7698, 7697])).
% 1.64/1.88 tff(7700,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7699, 77, 67, 3208])).
% 1.64/1.88 tff(7701,plain,
% 1.64/1.88 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[663, 21, 7700])).
% 1.64/1.88 tff(7702,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7701, 7693])).
% 1.64/1.88 tff(7703,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7704,plain,
% 1.64/1.88 (((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7705,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7704])).
% 1.64/1.88 tff(7706,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[7705, 7703])).
% 1.64/1.88 tff(7707,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7708,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7707, 7706])).
% 1.64/1.88 tff(7709,plain,
% 1.64/1.88 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7708, 77, 67, 3208])).
% 1.64/1.88 tff(7710,plain,
% 1.64/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7711,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7712,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7711, 7710])).
% 1.64/1.88 tff(7713,plain,
% 1.64/1.88 (b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7712, 21, 7692, 7709])).
% 1.64/1.88 tff(7714,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7715,plain,
% 1.64/1.88 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7716,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7715])).
% 1.64/1.88 tff(7717,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[7716, 7714])).
% 1.64/1.88 tff(7718,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7719,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7718, 7717])).
% 1.64/1.88 tff(7720,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7719, 116, 27, 7713, 7702, 7689])).
% 1.64/1.88 tff(7721,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(7722,plain,
% 1.64/1.88 (~r(s(s(elem!1)), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7721, 7247, 27, 67, 1331, 7246])).
% 1.64/1.88 tff(7723,plain,
% 1.64/1.88 (b(s(s(elem!1)), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3219, 7722])).
% 1.64/1.88 tff(7724,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7723, 7686])).
% 1.64/1.88 tff(7725,plain,((~(s(s(elem!1)) = elem!1)) | b(elem!1, z) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(7726,plain,
% 1.64/1.88 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7725, 7662, 7146, 64, 7653])).
% 1.64/1.88 tff(7727,plain,
% 1.64/1.88 (b(s(s(elem!1)), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[743, 7726, 7606])).
% 1.64/1.88 tff(7728,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 1.64/1.88 tff(7729,plain,
% 1.64/1.88 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7728])).
% 1.64/1.88 tff(7730,plain,
% 1.64/1.88 (s(s(s(z))) = s(elem!1)),
% 1.64/1.88 inference(transitivity,[status(thm)],[128, 7729, 520])).
% 1.64/1.88 tff(7731,plain,
% 1.64/1.88 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7730])).
% 1.64/1.88 tff(7732,plain,
% 1.64/1.88 (s(s(z)) = elem!1),
% 1.64/1.88 inference(transitivity,[status(thm)],[132, 7731, 460])).
% 1.64/1.88 tff(7733,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[422, 7732])).
% 1.64/1.88 tff(7734,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(7735,plain,
% 1.64/1.88 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7734, 7639])).
% 1.64/1.88 tff(7736,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7737,plain,
% 1.64/1.88 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7738,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7737])).
% 1.64/1.88 tff(7739,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[7738, 7736])).
% 1.64/1.88 tff(7740,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7741,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7740, 7739])).
% 1.64/1.88 tff(7742,plain,
% 1.64/1.88 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7741, 116, 7113, 1331, 5298, 845])).
% 1.64/1.88 tff(7743,plain,
% 1.64/1.88 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 7742])).
% 1.64/1.88 tff(7744,plain,
% 1.64/1.88 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.64/1.88 inference(commutativity,[status(thm)],[])).
% 1.64/1.88 tff(7745,plain,
% 1.64/1.88 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[7744])).
% 1.64/1.88 tff(7746,plain,
% 1.64/1.88 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7745])).
% 1.64/1.88 tff(7747,plain,
% 1.64/1.88 (~(s(s(elem!1)) = s(s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5936, 7746])).
% 1.64/1.88 tff(7748,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7749,plain,
% 1.64/1.88 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7750,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[7749])).
% 1.64/1.88 tff(7751,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[7750, 7748])).
% 1.64/1.88 tff(7752,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7753,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7752, 7751])).
% 1.64/1.88 tff(7754,plain,
% 1.64/1.88 (~b(s(s(elem!1)), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7753, 116, 616, 7113, 1331, 5298])).
% 1.64/1.88 tff(7755,plain,
% 1.64/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7756,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(7757,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[7756, 7755])).
% 1.64/1.88 tff(7758,plain,
% 1.64/1.88 ((s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7757, 21, 7754])).
% 1.64/1.88 tff(7759,plain,
% 1.64/1.88 (r(s(s(elem!1)), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[7758, 7747])).
% 1.64/1.88 tff(7760,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(7761,plain,
% 1.64/1.88 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7762,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7761])).
% 1.64/1.89 tff(7763,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7762, 7760])).
% 1.64/1.89 tff(7764,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7765,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7764, 7763])).
% 1.64/1.89 tff(7766,plain,
% 1.64/1.89 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7765, 77, 7759, 7743])).
% 1.64/1.89 tff(7767,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7768,plain,
% 1.64/1.89 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7769,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7768])).
% 1.64/1.89 tff(7770,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7769, 7767])).
% 1.64/1.89 tff(7771,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7772,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(elem!1, s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7771, 7770])).
% 1.64/1.89 tff(7773,plain,
% 1.64/1.89 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7772, 116, 616, 7113, 5298, 845])).
% 1.64/1.89 tff(7774,plain,
% 1.64/1.89 ((s(s(s(s(s(z))))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4828, 21, 7773])).
% 1.64/1.89 tff(7775,plain,
% 1.64/1.89 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7774, 7766])).
% 1.64/1.89 tff(7776,plain,
% 1.64/1.89 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7775])).
% 1.64/1.89 tff(7777,plain,
% 1.64/1.89 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[7776])).
% 1.64/1.89 tff(7778,plain,
% 1.64/1.89 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[561, 7777, 553])).
% 1.64/1.89 tff(7779,plain,
% 1.64/1.89 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7778])).
% 1.64/1.89 tff(7780,plain,
% 1.64/1.89 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(elem!1))),
% 1.64/1.89 inference(symmetry,[status(thm)],[7779])).
% 1.64/1.89 tff(7781,plain,
% 1.64/1.89 (~b(s(z), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7130, 116, 270, 271, 7113])).
% 1.64/1.89 tff(7782,plain,
% 1.64/1.89 (r(s(z), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[172, 7781])).
% 1.64/1.89 tff(7783,assumption,(~(s(s(s(s(z)))) = s(s(elem!1)))), introduced(assumption)).
% 1.64/1.89 tff(7784,plain,
% 1.64/1.89 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7778])).
% 1.64/1.89 tff(7785,plain,
% 1.64/1.89 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7784, 1580])).
% 1.64/1.89 tff(7786,plain,
% 1.64/1.89 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.64/1.89 inference(commutativity,[status(thm)],[])).
% 1.64/1.89 tff(7787,plain,
% 1.64/1.89 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[554, 7776, 520])).
% 1.64/1.89 tff(7788,plain,
% 1.64/1.89 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7787])).
% 1.64/1.89 tff(7789,plain,
% 1.64/1.89 (s(s(s(z))) = elem!1),
% 1.64/1.89 inference(transitivity,[status(thm)],[128, 7788, 460])).
% 1.64/1.89 tff(7790,plain,
% 1.64/1.89 ((s(s(s(z))) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7789])).
% 1.64/1.89 tff(7791,plain,
% 1.64/1.89 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[7790, 7786])).
% 1.64/1.89 tff(7792,plain,
% 1.64/1.89 ((s(s(s(z))) = s(elem!1)) <=> (elem!1 = s(s(s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7791, 7785])).
% 1.64/1.89 tff(7793,plain,
% 1.64/1.89 ((~(s(s(s(z))) = s(elem!1))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7792])).
% 1.64/1.89 tff(7794,plain,
% 1.64/1.89 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.64/1.89 inference(commutativity,[status(thm)],[])).
% 1.64/1.89 tff(7795,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7787])).
% 1.64/1.89 tff(7796,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7795, 7794])).
% 1.64/1.89 tff(7797,plain,
% 1.64/1.89 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7796])).
% 1.64/1.89 tff(7798,plain,
% 1.64/1.89 (~(s(s(s(z))) = s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1140, 7797])).
% 1.64/1.89 tff(7799,plain,
% 1.64/1.89 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7798, 7793])).
% 1.64/1.89 tff(7800,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1596, 3288, 2416])).
% 1.64/1.89 tff(7801,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7802,plain,
% 1.64/1.89 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7803,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7802])).
% 1.64/1.89 tff(7804,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7803, 7801])).
% 1.64/1.89 tff(7805,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7806,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7805, 7804])).
% 1.64/1.89 tff(7807,plain,
% 1.64/1.89 (~b(s(s(z)), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7806, 116, 616, 3813, 1331, 7800])).
% 1.64/1.89 tff(7808,plain,
% 1.64/1.89 (r(s(s(z)), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5939, 21, 5936, 7807])).
% 1.64/1.89 tff(7809,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7810,plain,
% 1.64/1.89 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7811,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7810])).
% 1.64/1.89 tff(7812,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7811, 7809])).
% 1.64/1.89 tff(7813,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7814,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7813, 7812])).
% 1.64/1.89 tff(7815,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7814, 116, 616, 3813, 28, 7800])).
% 1.64/1.89 tff(7816,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7817,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7818,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7817, 7816])).
% 1.64/1.89 tff(7819,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7818, 21, 7815, 7783])).
% 1.64/1.89 tff(7820,plain,
% 1.64/1.89 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4415, 3288, 1331, 1362, 3812])).
% 1.64/1.89 tff(7821,plain,
% 1.64/1.89 (r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[149, 7820])).
% 1.64/1.89 tff(7822,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7823,plain,
% 1.64/1.89 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7824,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7823])).
% 1.64/1.89 tff(7825,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7824, 7822])).
% 1.64/1.89 tff(7826,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(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(7827,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7826, 7825])).
% 1.64/1.89 tff(7828,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7827, 77, 7821, 7819, 7808])).
% 1.64/1.89 tff(7829,plain,((~r(s(s(s(s(z)))), z)) | (s(s(z)) = s(s(elem!1))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(7830,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7829, 7799, 7783, 575, 1331, 28, 616, 5936, 448])).
% 1.64/1.89 tff(7831,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[247, 7830])).
% 1.64/1.89 tff(7832,plain,
% 1.64/1.89 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[279, 7831, 270, 271])).
% 1.64/1.89 tff(7833,plain,
% 1.64/1.89 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[325, 7832])).
% 1.64/1.89 tff(7834,plain,
% 1.64/1.89 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[336, 7833, 7782])).
% 1.64/1.89 tff(7835,plain,
% 1.64/1.89 (b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[149, 7834])).
% 1.64/1.89 tff(7836,plain,
% 1.64/1.89 (b(s(s(z)), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7835, 7780])).
% 1.64/1.89 tff(7837,plain,
% 1.64/1.89 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7789])).
% 1.64/1.89 tff(7838,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7787])).
% 1.64/1.89 tff(7839,plain,
% 1.64/1.89 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[28, 7838])).
% 1.64/1.89 tff(7840,plain,
% 1.64/1.89 (b(s(elem!1), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7839, 7837])).
% 1.64/1.89 tff(7841,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7842,plain,
% 1.64/1.89 (((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7843,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7842])).
% 1.64/1.89 tff(7844,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7843, 7841])).
% 1.64/1.89 tff(7845,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7846,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7845, 7844])).
% 1.64/1.89 tff(7847,plain,
% 1.64/1.89 (~b(s(s(z)), s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7846, 116, 7113, 1331, 5298, 7840])).
% 1.64/1.89 tff(7848,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7847, 7836])).
% 1.64/1.89 tff(7849,plain,((~b(elem!1, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~r(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(7850,plain,
% 1.64/1.89 (~b(elem!1, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7849, 7735, 271, 7124, 7663, 7653, 28, 7727, 7684, 7599, 7683])).
% 1.64/1.89 tff(7851,plain,
% 1.64/1.89 (r(elem!1, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[6497, 7850, 7640])).
% 1.64/1.89 tff(7852,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7853,plain,
% 1.64/1.89 (((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7854,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7853])).
% 1.64/1.89 tff(7855,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7854, 7852])).
% 1.64/1.89 tff(7856,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7857,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7856, 7855])).
% 1.64/1.89 tff(7858,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7857, 77, 7605, 7851, 7132])).
% 1.64/1.89 tff(7859,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(s(s(s(z))), z) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(7860,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7859, 271, 292, 340, 57, 4432])).
% 1.64/1.89 tff(7861,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3951, 7860])).
% 1.64/1.89 tff(7862,plain,
% 1.64/1.89 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3975, 7861, 292])).
% 1.64/1.89 tff(7863,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[325, 7862])).
% 1.64/1.89 tff(7864,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3961, 7861, 64])).
% 1.64/1.89 tff(7865,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[247, 7864])).
% 1.64/1.89 tff(7866,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[279, 7865, 7863, 7124, 271])).
% 1.64/1.89 tff(7867,plain,((~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(s(s(s(z))), z) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(7868,plain,
% 1.64/1.89 (~b(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7867, 57, 340, 292, 4432])).
% 1.64/1.89 tff(7869,plain,
% 1.64/1.89 (r(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[289, 7868])).
% 1.64/1.89 tff(7870,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7871,plain,
% 1.64/1.89 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(7872,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[7871])).
% 1.64/1.89 tff(7873,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[7872, 7870])).
% 1.64/1.89 tff(7874,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(7875,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[7874, 7873])).
% 1.64/1.89 tff(7876,plain,
% 1.64/1.89 (~r(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[7875, 77, 7869, 7120])).
% 1.64/1.89 tff(7877,plain,
% 1.64/1.89 (b(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1174, 7876])).
% 1.64/1.89 tff(7878,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7879,plain,
% 1.74/1.90 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7880,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7879])).
% 1.74/1.90 tff(7881,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7880, 7878])).
% 1.74/1.90 tff(7882,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7883,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7882, 7881])).
% 1.74/1.90 tff(7884,plain,
% 1.74/1.90 (~b(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7883, 116, 7124, 7113, 7877])).
% 1.74/1.90 tff(7885,plain,
% 1.74/1.90 (r(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[172, 7884])).
% 1.74/1.90 tff(7886,plain,
% 1.74/1.90 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2319, 7885, 292])).
% 1.74/1.90 tff(7887,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[105, 7886])).
% 1.74/1.90 tff(7888,plain,
% 1.74/1.90 (~r(z, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[301, 7869, 292])).
% 1.74/1.90 tff(7889,plain,
% 1.74/1.90 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4749])).
% 1.74/1.90 tff(7890,plain,
% 1.74/1.90 (b(s(elem!1), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7113, 7889])).
% 1.74/1.90 tff(7891,plain,
% 1.74/1.90 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4751])).
% 1.74/1.90 tff(7892,plain,
% 1.74/1.90 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[7891])).
% 1.74/1.90 tff(7893,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4749])).
% 1.74/1.90 tff(7894,plain,
% 1.74/1.90 (b(s(elem!1), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[27, 7893])).
% 1.74/1.90 tff(7895,plain,
% 1.74/1.90 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7894, 7892])).
% 1.74/1.90 tff(7896,plain,
% 1.74/1.90 (~r(z, s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2486, 4759])).
% 1.74/1.90 tff(7897,plain,
% 1.74/1.90 (b(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[514, 7896])).
% 1.74/1.90 tff(7898,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1489, 4748, 67, 448])).
% 1.74/1.90 tff(7899,plain,
% 1.74/1.90 (~r(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7898, 4776])).
% 1.74/1.90 tff(7900,plain,
% 1.74/1.90 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7899, 4774])).
% 1.74/1.90 tff(7901,plain,
% 1.74/1.90 (b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[743, 4772, 7900])).
% 1.74/1.90 tff(7902,plain,
% 1.74/1.90 (b(elem!1, z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1458, 4748, 270])).
% 1.74/1.90 tff(7903,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7904,plain,
% 1.74/1.90 (((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7905,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7904])).
% 1.74/1.90 tff(7906,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7905, 7903])).
% 1.74/1.90 tff(7907,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7908,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7907, 7906])).
% 1.74/1.90 tff(7909,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7908, 116, 7902, 7901, 7897, 7895, 7890])).
% 1.74/1.90 tff(7910,plain,((~r(z, elem!1)) | r(z, s(s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | b(s(z), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7911,plain,
% 1.74/1.90 (~r(z, elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7910, 7888, 7887, 64, 7124, 340, 7869])).
% 1.74/1.90 tff(7912,plain,
% 1.74/1.90 (b(z, elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1044, 7911, 7136])).
% 1.74/1.90 tff(7913,plain,
% 1.74/1.90 (~(s(z) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4796, 7912, 7868])).
% 1.74/1.90 tff(7914,plain,
% 1.74/1.90 (r(s(z), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[357, 7913, 340])).
% 1.74/1.90 tff(7915,plain,
% 1.74/1.90 (~r(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[368, 7914, 292])).
% 1.74/1.90 tff(7916,plain,
% 1.74/1.90 (~r(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4008, 360, 156])).
% 1.74/1.90 tff(7917,plain,
% 1.74/1.90 (s(s(z)) = elem!1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[426, 1, 7916])).
% 1.74/1.90 tff(7918,plain,
% 1.74/1.90 (s(s(s(z))) = s(elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7917])).
% 1.74/1.90 tff(7919,plain,
% 1.74/1.90 (s(elem!1) = s(s(s(z)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[7918])).
% 1.74/1.90 tff(7920,plain,
% 1.74/1.90 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7919])).
% 1.74/1.90 tff(7921,plain,
% 1.74/1.90 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[7920])).
% 1.74/1.90 tff(7922,plain,
% 1.74/1.90 (b(elem!1, z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2403, 7917, 7113])).
% 1.74/1.90 tff(7923,plain,
% 1.74/1.90 (~(elem!1 = s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1470, 7922, 57])).
% 1.74/1.90 tff(7924,plain,
% 1.74/1.90 (b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1345, 7923, 4094])).
% 1.74/1.90 tff(7925,plain,
% 1.74/1.90 (b(elem!1, s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7924, 7921])).
% 1.74/1.90 tff(7926,plain,
% 1.74/1.90 (b(z, elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1044, 1052, 7422])).
% 1.74/1.90 tff(7927,plain,
% 1.74/1.90 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[529, 7917, 7422])).
% 1.74/1.90 tff(7928,plain,
% 1.74/1.90 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[557])).
% 1.74/1.90 tff(7929,plain,
% 1.74/1.90 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[7928])).
% 1.74/1.90 tff(7930,plain,
% 1.74/1.90 (r(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[327, 7929])).
% 1.74/1.90 tff(7931,assumption,(~r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.90 tff(7932,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7931, 7930])).
% 1.74/1.90 tff(7933,plain,(r(s(z), s(s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7934,plain,
% 1.74/1.90 (r(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7933, 327, 370])).
% 1.74/1.90 tff(7935,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[370])).
% 1.74/1.90 tff(7936,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7935, 3811])).
% 1.74/1.90 tff(7937,plain,
% 1.74/1.90 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[336, 327, 156])).
% 1.74/1.90 tff(7938,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[149, 7937])).
% 1.74/1.90 tff(7939,plain,
% 1.74/1.90 (b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7938, 7936])).
% 1.74/1.90 tff(7940,plain,
% 1.74/1.90 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7534, 7934, 360])).
% 1.74/1.90 tff(7941,plain,
% 1.74/1.90 (b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[743, 7940, 574])).
% 1.74/1.90 tff(7942,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7943,plain,
% 1.74/1.90 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7944,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7943])).
% 1.74/1.90 tff(7945,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7944, 7942])).
% 1.74/1.90 tff(7946,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7947,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7946, 7945])).
% 1.74/1.90 tff(7948,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7947, 116, 1055, 616, 668, 1879])).
% 1.74/1.90 tff(7949,plain,((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7950,plain,
% 1.74/1.90 (~b(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7949, 7941, 1055, 7939])).
% 1.74/1.90 tff(7951,plain,
% 1.74/1.90 (r(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[514, 7950])).
% 1.74/1.90 tff(7952,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7953,plain,
% 1.74/1.90 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z)))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7954,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7953])).
% 1.74/1.90 tff(7955,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7954, 7952])).
% 1.74/1.90 tff(7956,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7957,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7956, 7955])).
% 1.74/1.90 tff(7958,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7957, 77, 360, 7951, 293, 7934])).
% 1.74/1.90 tff(7959,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~r(z, s(z))) | (~b(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~(s(s(z)) = elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7960,plain,
% 1.74/1.90 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7959, 7927, 293, 7926, 360, 7917, 156])).
% 1.74/1.90 tff(7961,plain,
% 1.74/1.90 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[325, 7960])).
% 1.74/1.90 tff(7962,plain,
% 1.74/1.90 (~b(elem!1, z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4732, 7926, 270, 249, 254])).
% 1.74/1.90 tff(7963,plain,
% 1.74/1.90 (~(s(s(z)) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2403, 7962, 7113])).
% 1.74/1.90 tff(7964,plain,
% 1.74/1.90 (~(s(z) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1980, 1052, 249, 254, 270])).
% 1.74/1.90 tff(7965,plain,
% 1.74/1.90 (r(s(z), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[357, 7964, 340])).
% 1.74/1.90 tff(7966,plain,
% 1.74/1.90 (~r(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4008, 7965, 156])).
% 1.74/1.90 tff(7967,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[426, 7966, 7963, 1])).
% 1.74/1.90 tff(7968,plain,(r(z, elem!1) | b(s(s(z)), elem!1) | (~r(s(z), s(s(z)))) | b(s(z), elem!1) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7969,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7968, 7961, 156, 340, 270, 1052, 1])).
% 1.74/1.90 tff(7970,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[247, 7969])).
% 1.74/1.90 tff(7971,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3961, 7970, 64])).
% 1.74/1.90 tff(7972,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3951, 7971])).
% 1.74/1.90 tff(7973,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3257, 7972, 7917])).
% 1.74/1.90 tff(7974,plain,
% 1.74/1.90 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[608, 7917])).
% 1.74/1.90 tff(7975,plain,
% 1.74/1.90 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7918])).
% 1.74/1.90 tff(7976,plain,
% 1.74/1.90 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[7975])).
% 1.74/1.90 tff(7977,plain,
% 1.74/1.90 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7976])).
% 1.74/1.90 tff(7978,plain,
% 1.74/1.90 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7918])).
% 1.74/1.90 tff(7979,plain,
% 1.74/1.90 (r(s(elem!1), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[64, 7978])).
% 1.74/1.90 tff(7980,plain,
% 1.74/1.90 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7918])).
% 1.74/1.90 tff(7981,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7980])).
% 1.74/1.90 tff(7982,plain,
% 1.74/1.90 (r(s(s(elem!1)), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7970, 7981])).
% 1.74/1.90 tff(7983,plain,
% 1.74/1.90 (~r(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7563, 77, 7982, 7979])).
% 1.74/1.90 tff(7984,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7983, 7977])).
% 1.74/1.90 tff(7985,plain,
% 1.74/1.90 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[664, 7984, 7974])).
% 1.74/1.90 tff(7986,plain,
% 1.74/1.90 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4150, 7985, 7917])).
% 1.74/1.90 tff(7987,plain,
% 1.74/1.90 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[568, 7917])).
% 1.74/1.90 tff(7988,plain,
% 1.74/1.90 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[836, 7917, 7927])).
% 1.74/1.90 tff(7989,plain,
% 1.74/1.90 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4300, 116, 1055, 7540, 845])).
% 1.74/1.90 tff(7990,plain,
% 1.74/1.90 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[898, 21, 895, 7989])).
% 1.74/1.90 tff(7991,plain,
% 1.74/1.90 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4643, 77, 5326, 7990])).
% 1.74/1.90 tff(7992,plain,
% 1.74/1.90 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[858, 21, 855, 7991])).
% 1.74/1.90 tff(7993,plain,
% 1.74/1.90 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[555])).
% 1.74/1.90 tff(7994,plain,
% 1.74/1.90 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[576])).
% 1.74/1.90 tff(7995,plain,
% 1.74/1.90 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7994])).
% 1.74/1.90 tff(7996,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7997,plain,
% 1.74/1.90 (((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7998,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7997])).
% 1.74/1.90 tff(7999,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7998, 7996])).
% 1.74/1.90 tff(8000,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(8001,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8000, 7999])).
% 1.74/1.90 tff(8002,plain,
% 1.74/1.90 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[8001, 77, 5326, 7990])).
% 1.74/1.90 tff(8003,plain,
% 1.74/1.90 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8002, 7995])).
% 1.74/1.90 tff(8004,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)],[1380, 8003])).
% 1.74/1.90 tff(8005,plain,
% 1.74/1.90 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[8004, 7993])).
% 1.74/1.90 tff(8006,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8007,plain,
% 1.74/1.90 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(8008,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8007])).
% 1.74/1.91 tff(8009,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8008, 8006])).
% 1.74/1.91 tff(8010,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8011,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8010, 8009])).
% 1.74/1.91 tff(8012,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8011, 116, 4041, 845, 8005, 7992])).
% 1.74/1.91 tff(8013,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~(s(s(z)) = elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8014,plain,
% 1.74/1.91 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8013, 7925, 7917, 7988, 7979, 7926])).
% 1.74/1.91 tff(8015,plain,
% 1.74/1.91 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[885, 8014, 7987])).
% 1.74/1.91 tff(8016,plain,
% 1.74/1.91 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[7980])).
% 1.74/1.91 tff(8017,plain,
% 1.74/1.91 (b(s(z), s(s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7961, 8016])).
% 1.74/1.91 tff(8018,plain,
% 1.74/1.91 (~b(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4610, 752, 370, 4602, 1027, 360])).
% 1.74/1.91 tff(8019,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[808, 8018, 1416])).
% 1.74/1.91 tff(8020,plain,((~r(s(s(elem!1)), elem!1)) | (~(s(s(z)) = elem!1)) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8021,plain,
% 1.74/1.91 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8020, 7917, 8017, 8015, 360])).
% 1.74/1.91 tff(8022,plain,
% 1.74/1.91 (b(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[743, 8021, 7927])).
% 1.74/1.91 tff(8023,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8024,plain,
% 1.74/1.91 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8025,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8024])).
% 1.74/1.91 tff(8026,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8025, 8023])).
% 1.74/1.91 tff(8027,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8028,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 1.74/1.91 tff(8029,plain,
% 1.74/1.91 (~b(z, s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8028, 116, 7926, 7922, 8022])).
% 1.74/1.91 tff(8030,plain,
% 1.74/1.91 (r(z, s(s(elem!1)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[514, 8029])).
% 1.74/1.91 tff(8031,plain,
% 1.74/1.91 (~r(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3185, 8030, 293])).
% 1.74/1.91 tff(8032,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[808, 8031])).
% 1.74/1.91 tff(8033,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8034,plain,
% 1.74/1.91 (((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8035,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8034])).
% 1.74/1.91 tff(8036,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8035, 8033])).
% 1.74/1.91 tff(8037,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8038,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8037, 8036])).
% 1.74/1.91 tff(8039,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8038, 116, 8032, 8022, 7986, 7973, 7925])).
% 1.74/1.91 tff(8040,plain,(b(s(s(z)), elem!1) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | b(s(z), elem!1) | (~b(s(z), z)) | r(z, elem!1) | r(elem!1, s(s(s(z)))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8041,plain,
% 1.74/1.91 (b(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8040, 7869, 7914, 7885, 340, 7124, 7911, 7915, 57])).
% 1.74/1.91 tff(8042,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2658, 116, 1055, 537, 7113, 1331])).
% 1.74/1.91 tff(8043,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8044,plain,
% 1.74/1.91 (~b(elem!1, z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8043, 7912, 8041])).
% 1.74/1.91 tff(8045,plain,
% 1.74/1.91 (~(s(s(z)) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2403, 8044, 7113])).
% 1.74/1.91 tff(8046,plain,
% 1.74/1.91 (r(elem!1, z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[545, 8044, 7135])).
% 1.74/1.91 tff(8047,plain,
% 1.74/1.91 (elem!1 = s(s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2824, 575, 7113, 1055, 1331, 353, 422, 340])).
% 1.74/1.91 tff(8048,plain,
% 1.74/1.91 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8047])).
% 1.74/1.91 tff(8049,plain,
% 1.74/1.91 (~r(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2095, 575, 293])).
% 1.74/1.91 tff(8050,plain,
% 1.74/1.91 (b(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[633, 8049, 421])).
% 1.74/1.91 tff(8051,plain,
% 1.74/1.91 (b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8050, 8048])).
% 1.74/1.91 tff(8052,plain,
% 1.74/1.91 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8047])).
% 1.74/1.91 tff(8053,plain,
% 1.74/1.91 (b(z, s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1055, 8052])).
% 1.74/1.91 tff(8054,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8055,plain,
% 1.74/1.91 (((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8056,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8055])).
% 1.74/1.91 tff(8057,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8056, 8054])).
% 1.74/1.91 tff(8058,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8059,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8058, 8057])).
% 1.74/1.91 tff(8060,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8059, 116, 270, 8053, 27, 2442, 8051])).
% 1.74/1.91 tff(8061,plain,((~r(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | (s(s(z)) = elem!1) | b(s(z), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8062,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8061, 8046, 8045, 7887, 7877, 7912, 8041, 7913, 7124, 340, 7869])).
% 1.74/1.91 tff(8063,plain,(b(s(s(s(z))), z) | b(s(z), elem!1) | (~r(s(z), s(s(s(z))))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8064,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8063, 292, 340, 4432])).
% 1.74/1.91 tff(8065,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8066,plain,
% 1.74/1.91 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8067,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8066])).
% 1.74/1.91 tff(8068,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8067, 8065])).
% 1.74/1.91 tff(8069,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8070,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8069, 8068])).
% 1.74/1.91 tff(8071,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8070, 77, 155, 2235, 292, 3651])).
% 1.74/1.91 tff(8072,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8073,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8072, 3406, 292, 7120])).
% 1.74/1.91 tff(8074,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[105, 8073])).
% 1.74/1.91 tff(8075,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1784])).
% 1.74/1.91 tff(8076,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[27, 8075])).
% 1.74/1.91 tff(8077,plain,
% 1.74/1.91 (b(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7116, 1713, 7113])).
% 1.74/1.91 tff(8078,plain,
% 1.74/1.91 (~(s(z) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4434, 8077, 4432])).
% 1.74/1.91 tff(8079,plain,
% 1.74/1.91 (r(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[357, 8078, 340])).
% 1.74/1.91 tff(8080,plain,
% 1.74/1.91 (~r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[368, 8079, 292])).
% 1.74/1.91 tff(8081,plain,
% 1.74/1.91 (~(elem!1 = s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2407, 3545, 8064])).
% 1.74/1.91 tff(8082,plain,
% 1.74/1.91 (b(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1345, 8081, 8080])).
% 1.74/1.91 tff(8083,plain,
% 1.74/1.91 (b(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8064, 3547])).
% 1.74/1.91 tff(8084,plain,
% 1.74/1.91 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[442])).
% 1.74/1.91 tff(8085,plain,
% 1.74/1.91 (b(s(s(elem!1)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7170, 1713, 7113])).
% 1.74/1.91 tff(8086,plain,
% 1.74/1.91 (b(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8085, 8084])).
% 1.74/1.91 tff(8087,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8088,plain,
% 1.74/1.91 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8089,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8088])).
% 1.74/1.91 tff(8090,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8089, 8087])).
% 1.74/1.91 tff(8091,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8092,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8091, 8090])).
% 1.74/1.91 tff(8093,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8092, 116, 8086, 8083, 8082, 8076])).
% 1.74/1.91 tff(8094,plain,((~(z = elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8095,plain,
% 1.74/1.91 (~(z = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8094, 8074, 292, 340, 4432])).
% 1.74/1.91 tff(8096,plain,
% 1.74/1.91 (r(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[426, 2845, 1])).
% 1.74/1.91 tff(8097,plain,
% 1.74/1.91 (~b(elem!1, z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1992, 1985, 1989])).
% 1.74/1.91 tff(8098,plain,
% 1.74/1.91 (r(elem!1, z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[545, 8097, 534])).
% 1.74/1.91 tff(8099,plain,
% 1.74/1.91 (~r(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2815, 575, 155])).
% 1.74/1.91 tff(8100,plain,
% 1.74/1.91 (s(z) = elem!1),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[357, 8099, 340])).
% 1.74/1.91 tff(8101,plain,
% 1.74/1.91 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1531, 8100])).
% 1.74/1.91 tff(8102,plain,
% 1.74/1.91 (s(s(z)) = s(elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8100])).
% 1.74/1.91 tff(8103,plain,
% 1.74/1.91 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8102])).
% 1.74/1.91 tff(8104,plain,
% 1.74/1.91 (b(s(elem!1), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7113, 8103])).
% 1.74/1.91 tff(8105,plain,
% 1.74/1.91 (s(s(s(z))) = s(s(elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8102])).
% 1.74/1.91 tff(8106,plain,
% 1.74/1.91 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[8105])).
% 1.74/1.91 tff(8107,plain,
% 1.74/1.91 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8106])).
% 1.74/1.91 tff(8108,plain,
% 1.74/1.91 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[8107])).
% 1.74/1.91 tff(8109,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8102])).
% 1.74/1.91 tff(8110,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8109, 8108])).
% 1.74/1.91 tff(8111,plain,
% 1.74/1.91 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8100])).
% 1.74/1.91 tff(8112,plain,
% 1.74/1.91 (r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[292, 8111])).
% 1.74/1.91 tff(8113,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5025, 8112, 428])).
% 1.74/1.91 tff(8114,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[105, 8113])).
% 1.74/1.91 tff(8115,plain,
% 1.74/1.91 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8114, 8110])).
% 1.74/1.91 tff(8116,plain,
% 1.74/1.91 (b(s(s(elem!1)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2832, 8100, 2247])).
% 1.74/1.91 tff(8117,plain,
% 1.74/1.91 (s(elem!1) = s(s(z))),
% 1.74/1.91 inference(symmetry,[status(thm)],[8102])).
% 1.74/1.91 tff(8118,plain,
% 1.74/1.91 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8117])).
% 1.74/1.91 tff(8119,plain,
% 1.74/1.91 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[8118])).
% 1.74/1.91 tff(8120,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8121,plain,
% 1.74/1.91 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8122,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8121])).
% 1.74/1.91 tff(8123,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8122, 8120])).
% 1.74/1.91 tff(8124,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8125,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8124, 8123])).
% 1.74/1.91 tff(8126,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8125, 116, 2247, 1303, 27, 2442])).
% 1.74/1.91 tff(8127,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8128,plain,
% 1.74/1.91 (~b(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8127, 8114, 7113, 2247])).
% 1.74/1.91 tff(8129,plain,
% 1.74/1.91 (r(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1174, 8128])).
% 1.74/1.91 tff(8130,plain,
% 1.74/1.91 (r(z, s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8129, 8119])).
% 1.74/1.91 tff(8131,plain,
% 1.74/1.91 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8102])).
% 1.74/1.91 tff(8132,plain,
% 1.74/1.91 (r(s(elem!1), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[428, 8131])).
% 1.74/1.91 tff(8133,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.74/1.92 tff(8134,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8135,plain,
% 1.74/1.92 (((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8136,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8135])).
% 1.74/1.92 tff(8137,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8136, 8134])).
% 1.74/1.92 tff(8138,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8139,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8138, 8137])).
% 1.74/1.92 tff(8140,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8139, 77, 448, 650, 8133])).
% 1.74/1.92 tff(8141,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8142,plain,
% 1.74/1.92 (~r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8141, 8132, 8130])).
% 1.74/1.92 tff(8143,plain,
% 1.74/1.92 (b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8142, 518])).
% 1.74/1.92 tff(8144,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8145,plain,
% 1.74/1.92 (((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8146,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8145])).
% 1.74/1.92 tff(8147,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8146, 8144])).
% 1.74/1.92 tff(8148,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8149,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8148, 8147])).
% 1.74/1.92 tff(8150,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8149, 116, 1055, 1054, 573, 1878, 2844])).
% 1.74/1.92 tff(8151,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8152,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8151, 8143, 8116, 8115, 8104])).
% 1.74/1.92 tff(8153,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1068, 8152, 8101])).
% 1.74/1.92 tff(8154,plain,
% 1.74/1.92 (b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4796, 8143, 8100])).
% 1.74/1.92 tff(8155,plain,
% 1.74/1.92 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8105])).
% 1.74/1.92 tff(8156,plain,
% 1.74/1.92 (r(elem!1, s(s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8112, 8155])).
% 1.74/1.92 tff(8157,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5171, 8153, 8156, 8100])).
% 1.74/1.92 tff(8158,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3951, 8157])).
% 1.74/1.92 tff(8159,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3723, 8158, 2247, 8114, 8154])).
% 1.74/1.92 tff(8160,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[226, 8159])).
% 1.74/1.92 tff(8161,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2671, 8153, 575])).
% 1.74/1.92 tff(8162,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[247, 8161])).
% 1.74/1.92 tff(8163,plain,
% 1.74/1.92 (~b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3422, 8158, 8162, 2247, 8154])).
% 1.74/1.92 tff(8164,plain,
% 1.74/1.92 (r(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[172, 8163])).
% 1.74/1.92 tff(8165,plain,
% 1.74/1.92 (r(elem!1, s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2959, 8164, 8100])).
% 1.74/1.92 tff(8166,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4263, 8165, 8160, 8100, 8153])).
% 1.74/1.92 tff(8167,plain,((~r(elem!1, z)) | (~b(s(s(s(z))), z)) | (z = elem!1) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8168,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8167, 8098, 8096, 518, 2247, 292, 340, 3406])).
% 1.74/1.92 tff(8169,plain,((~(s(z) = elem!1)) | (z = elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(s(s(z)), elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8170,plain,
% 1.74/1.92 (~(s(z) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8169, 1, 2247, 292, 340, 518, 1989])).
% 1.74/1.92 tff(8171,plain,
% 1.74/1.92 (r(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[357, 8170, 340])).
% 1.74/1.92 tff(8172,plain,
% 1.74/1.92 (~r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[368, 8171, 292])).
% 1.74/1.92 tff(8173,plain,
% 1.74/1.92 (~r(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2815, 8171, 3406])).
% 1.74/1.92 tff(8174,plain,
% 1.74/1.92 (b(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[545, 8173, 534])).
% 1.74/1.92 tff(8175,plain,
% 1.74/1.92 (~r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[690, 8171, 3406])).
% 1.74/1.92 tff(8176,plain,
% 1.74/1.92 (b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8175, 518])).
% 1.74/1.92 tff(8177,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5469, 8176, 2247, 8174])).
% 1.74/1.92 tff(8178,plain,
% 1.74/1.92 (elem!1 = s(s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1345, 8177, 8172])).
% 1.74/1.92 tff(8179,plain,
% 1.74/1.92 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8178])).
% 1.74/1.92 tff(8180,plain,
% 1.74/1.92 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[8179])).
% 1.74/1.92 tff(8181,plain,
% 1.74/1.92 (b(s(s(z)), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[27, 8180])).
% 1.74/1.92 tff(8182,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1, 8181])).
% 1.74/1.92 tff(8183,plain,(b(s(s(z)), elem!1) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (z = elem!1) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8184,plain,
% 1.74/1.92 (b(s(s(z)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8183, 8074, 8064, 8095, 292, 340, 1989])).
% 1.74/1.92 tff(8185,plain,
% 1.74/1.92 (~(s(z) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4434, 8184, 4432])).
% 1.74/1.92 tff(8186,plain,
% 1.74/1.92 (r(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[357, 8185, 340])).
% 1.74/1.92 tff(8187,plain,
% 1.74/1.92 (~r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[690, 8186, 3406])).
% 1.74/1.92 tff(8188,plain,
% 1.74/1.92 (b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8187, 8095])).
% 1.74/1.92 tff(8189,plain,
% 1.74/1.92 (~(elem!1 = z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[533, 8095])).
% 1.74/1.92 tff(8190,plain,
% 1.74/1.92 (~r(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2815, 8186, 3406])).
% 1.74/1.92 tff(8191,plain,
% 1.74/1.92 (b(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[545, 8190, 8189])).
% 1.74/1.92 tff(8192,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8043, 8191, 8188, 8184])).
% 1.74/1.92 tff(8193,plain,(b(s(z), z) | b(s(z), elem!1) | b(s(s(z)), s(z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8194,plain,
% 1.74/1.92 (b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8193, 292, 4432, 340])).
% 1.74/1.92 tff(8195,plain,
% 1.74/1.92 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1474])).
% 1.74/1.92 tff(8196,plain,
% 1.74/1.92 (r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[292, 5697])).
% 1.74/1.92 tff(8197,plain,
% 1.74/1.92 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5025, 8196, 8096])).
% 1.74/1.92 tff(8198,plain,
% 1.74/1.92 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[105, 8197])).
% 1.74/1.92 tff(8199,plain,
% 1.74/1.92 (~b(z, s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8127, 8198, 7113, 2247])).
% 1.74/1.92 tff(8200,plain,
% 1.74/1.92 (r(z, s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1174, 8199])).
% 1.74/1.92 tff(8201,plain,
% 1.74/1.92 (r(z, s(elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8200, 8195])).
% 1.74/1.92 tff(8202,plain,
% 1.74/1.92 (r(s(elem!1), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8096, 1523])).
% 1.74/1.92 tff(8203,plain,
% 1.74/1.92 (~b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2936, 8198, 7113, 2247, 270])).
% 1.74/1.92 tff(8204,plain,
% 1.74/1.92 (~b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4796, 8203, 466])).
% 1.74/1.92 tff(8205,plain,
% 1.74/1.92 (r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8204, 518])).
% 1.74/1.92 tff(8206,plain,
% 1.74/1.92 (~r(z, s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8141, 8205, 8202])).
% 1.74/1.92 tff(8207,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8206, 8201])).
% 1.74/1.92 tff(8208,plain,((~(s(z) = elem!1)) | (z = elem!1) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8209,plain,
% 1.74/1.92 (~(s(z) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8208, 1, 2247, 270, 292, 7422])).
% 1.74/1.92 tff(8210,plain,
% 1.74/1.92 (r(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[357, 8209, 340])).
% 1.74/1.92 tff(8211,plain,
% 1.74/1.92 (~r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[368, 8210, 292])).
% 1.74/1.92 tff(8212,plain,
% 1.74/1.92 (~(s(s(z)) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2403, 1455, 7113])).
% 1.74/1.92 tff(8213,plain,
% 1.74/1.92 (r(s(s(z)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[426, 8212, 1])).
% 1.74/1.92 tff(8214,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5476, 77, 3469, 8213, 3651])).
% 1.74/1.92 tff(8215,plain,(b(elem!1, z) | (~r(s(s(z)), s(z))) | b(s(z), elem!1) | b(s(s(z)), elem!1) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8216,plain,
% 1.74/1.92 (b(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8215, 1, 340, 3651, 270])).
% 1.74/1.92 tff(8217,plain,
% 1.74/1.92 (~r(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4006, 77, 360, 428])).
% 1.74/1.92 tff(8218,plain,
% 1.74/1.92 (b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[170, 21, 54, 8217])).
% 1.74/1.92 tff(8219,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8220,plain,
% 1.74/1.92 (((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8221,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8220])).
% 1.74/1.92 tff(8222,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8221, 8219])).
% 1.74/1.92 tff(8223,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8224,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 1.74/1.92 tff(8225,plain,
% 1.74/1.92 (~r(z, s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8224, 77, 448, 428])).
% 1.74/1.92 tff(8226,plain,
% 1.74/1.92 (b(z, s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1174, 8225])).
% 1.74/1.92 tff(8227,plain,
% 1.74/1.92 (~r(s(s(z)), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[454, 77, 448, 428])).
% 1.74/1.92 tff(8228,plain,
% 1.74/1.92 (b(s(s(z)), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[25, 8227])).
% 1.74/1.92 tff(8229,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[7883, 116, 2920, 8228, 8226, 8218])).
% 1.74/1.92 tff(8230,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8231,plain,
% 1.74/1.92 (~r(s(s(z)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8230, 448, 360])).
% 1.74/1.92 tff(8232,plain,
% 1.74/1.92 (s(s(z)) = elem!1),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[426, 8231, 1])).
% 1.74/1.92 tff(8233,plain,
% 1.74/1.92 (~r(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2940, 448, 7113, 2247, 360])).
% 1.74/1.92 tff(8234,plain,
% 1.74/1.92 (b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[172, 8233])).
% 1.74/1.92 tff(8235,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[376, 8234, 8232, 340])).
% 1.74/1.92 tff(8236,plain,((~r(z, elem!1)) | b(s(z), elem!1) | b(s(s(z)), elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8237,plain,
% 1.74/1.92 (~r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8236, 1, 340, 2247, 8210])).
% 1.74/1.92 tff(8238,plain,
% 1.74/1.92 (b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8237, 7422])).
% 1.74/1.92 tff(8239,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5469, 8238, 2247, 8216])).
% 1.74/1.92 tff(8240,plain,
% 1.74/1.92 (elem!1 = s(s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1345, 8239, 8211])).
% 1.74/1.92 tff(8241,plain,
% 1.74/1.92 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8240])).
% 1.74/1.92 tff(8242,plain,
% 1.74/1.92 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[8241])).
% 1.74/1.92 tff(8243,plain,
% 1.74/1.92 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8242])).
% 1.74/1.92 tff(8244,plain,
% 1.74/1.92 (~(s(s(z)) = elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[100, 8243])).
% 1.74/1.92 tff(8245,plain,
% 1.74/1.92 (r(s(s(z)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[426, 8244, 1])).
% 1.74/1.92 tff(8246,plain,
% 1.74/1.92 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8240])).
% 1.74/1.92 tff(8247,plain,
% 1.74/1.92 (b(z, s(s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8238, 8246])).
% 1.74/1.92 tff(8248,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8249,plain,
% 1.74/1.92 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8250,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8249])).
% 1.74/1.92 tff(8251,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8250, 8248])).
% 1.74/1.92 tff(8252,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8253,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8252, 8251])).
% 1.74/1.92 tff(8254,plain,
% 1.74/1.92 (~b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8253, 116, 270, 2247, 8247, 7113])).
% 1.74/1.92 tff(8255,plain,
% 1.74/1.92 (r(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[172, 8254])).
% 1.74/1.92 tff(8256,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4008, 8255, 8245, 8210])).
% 1.74/1.92 tff(8257,plain,(b(s(s(z)), elem!1) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | b(s(z), elem!1) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8258,plain,
% 1.74/1.92 (b(s(s(z)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8257, 8194, 8064, 340, 292, 7120])).
% 1.74/1.92 tff(8259,plain,
% 1.74/1.92 (~(s(z) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4434, 8258, 4432])).
% 1.74/1.92 tff(8260,plain,
% 1.74/1.92 (r(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[357, 8259, 340])).
% 1.74/1.92 tff(8261,plain,
% 1.74/1.92 (~(elem!1 = z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[409, 8194, 340])).
% 1.74/1.92 tff(8262,plain,
% 1.74/1.92 (~(z = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[445, 8261])).
% 1.74/1.92 tff(8263,plain,
% 1.74/1.92 (~b(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8043, 1055, 1331])).
% 1.74/1.92 tff(8264,plain,
% 1.74/1.92 (~(s(s(z)) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2403, 8263, 7113])).
% 1.74/1.92 tff(8265,plain,
% 1.74/1.92 (r(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[545, 8263, 439])).
% 1.74/1.92 tff(8266,plain,
% 1.74/1.92 (~(elem!1 = s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2407, 8263, 2247])).
% 1.74/1.92 tff(8267,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2824, 8266, 8265, 7113, 1331, 1055, 353, 8264, 340])).
% 1.74/1.92 tff(8268,plain,((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | b(s(z), elem!1) | (~b(s(s(s(z))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8269,plain,
% 1.74/1.92 (~b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8268, 8258, 8259, 340, 8064, 8261])).
% 1.74/1.92 tff(8270,plain,
% 1.74/1.92 (r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8269, 8262])).
% 1.74/1.92 tff(8271,plain,
% 1.74/1.92 (~r(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3295, 8270, 8260])).
% 1.74/1.92 tff(8272,plain,
% 1.74/1.92 (b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[289, 8271])).
% 1.74/1.92 tff(8273,plain,
% 1.74/1.92 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[7144, 8272, 7113, 292])).
% 1.74/1.92 tff(8274,plain,
% 1.74/1.92 (~b(s(s(z)), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2936, 8272, 7113, 8064, 8194])).
% 1.74/1.92 tff(8275,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[105, 8274, 8273])).
% 1.74/1.92 tff(8276,plain,((~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8277,plain,
% 1.74/1.92 (~r(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8276, 340, 4432])).
% 1.74/1.92 tff(8278,plain,
% 1.74/1.92 (b(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[194, 8277])).
% 1.74/1.92 tff(8279,plain,
% 1.74/1.92 (~(elem!1 = z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[7116, 1, 7113])).
% 1.74/1.92 tff(8280,plain,
% 1.74/1.92 (~(z = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[445, 8279])).
% 1.74/1.92 tff(8281,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5476, 77, 360, 428, 3651])).
% 1.74/1.92 tff(8282,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8283,plain,
% 1.74/1.92 (~r(s(s(z)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8282, 360, 3651])).
% 1.74/1.92 tff(8284,plain,
% 1.74/1.92 (s(s(z)) = elem!1),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[426, 8283, 1])).
% 1.74/1.92 tff(8285,plain,
% 1.74/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[529, 8284, 8280])).
% 1.74/1.92 tff(8286,plain,
% 1.74/1.92 (s(s(s(z))) = s(elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8284])).
% 1.74/1.92 tff(8287,plain,
% 1.74/1.92 (s(elem!1) = s(s(s(z)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[8286])).
% 1.74/1.92 tff(8288,plain,
% 1.74/1.92 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8287])).
% 1.74/1.92 tff(8289,plain,
% 1.74/1.92 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.74/1.92 inference(symmetry,[status(thm)],[8288])).
% 1.74/1.92 tff(8290,plain,
% 1.74/1.92 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8287])).
% 1.74/1.92 tff(8291,plain,
% 1.74/1.92 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8290])).
% 1.74/1.92 tff(8292,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8286])).
% 1.74/1.92 tff(8293,plain,
% 1.74/1.92 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[608, 8284])).
% 1.74/1.92 tff(8294,plain,
% 1.74/1.92 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8286])).
% 1.74/1.92 tff(8295,plain,
% 1.74/1.92 (b(s(z), s(elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[175, 8294])).
% 1.74/1.92 tff(8296,plain,
% 1.74/1.92 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8286])).
% 1.74/1.92 tff(8297,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2136, 3406, 67])).
% 1.74/1.92 tff(8298,plain,
% 1.74/1.92 (b(s(s(s(z))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[402, 21, 135, 8297])).
% 1.74/1.92 tff(8299,plain,
% 1.74/1.92 (b(s(elem!1), s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8298, 8296])).
% 1.74/1.92 tff(8300,plain,
% 1.74/1.92 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8286])).
% 1.74/1.92 tff(8301,plain,
% 1.74/1.92 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[8300])).
% 1.74/1.92 tff(8302,plain,
% 1.74/1.92 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8301])).
% 1.74/1.92 tff(8303,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[8302])).
% 1.74/1.92 tff(8304,plain,
% 1.74/1.92 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[836, 8284, 8285])).
% 1.74/1.92 tff(8305,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[855, 1078])).
% 1.74/1.92 tff(8306,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8307,plain,
% 1.74/1.92 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8306, 8304])).
% 1.74/1.92 tff(8308,plain,
% 1.74/1.92 (~r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[690, 360, 3406])).
% 1.74/1.92 tff(8309,plain,
% 1.74/1.92 (b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8308, 8280])).
% 1.74/1.92 tff(8310,plain,
% 1.74/1.92 (~r(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2815, 360, 3406])).
% 1.74/1.92 tff(8311,plain,
% 1.74/1.92 (b(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[545, 8310, 8279])).
% 1.74/1.92 tff(8312,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8313,plain,
% 1.74/1.92 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8314,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8313])).
% 1.74/1.92 tff(8315,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8314, 8312])).
% 1.74/1.92 tff(8316,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8317,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8316, 8315])).
% 1.74/1.92 tff(8318,plain,
% 1.74/1.92 (~r(s(s(z)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8317, 77, 360, 155, 66])).
% 1.74/1.92 tff(8319,plain,
% 1.74/1.92 (b(s(z), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[172, 5941])).
% 1.74/1.92 tff(8320,plain,
% 1.74/1.92 (~b(s(s(z)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2282, 8319, 228, 155, 66])).
% 1.74/1.92 tff(8321,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[391, 21, 8320, 388, 8318])).
% 1.74/1.92 tff(8322,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8323,plain,
% 1.74/1.92 (~r(s(s(z)), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8322, 228, 155, 360])).
% 1.74/1.92 tff(8324,plain,
% 1.74/1.92 (b(s(s(z)), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[25, 8323])).
% 1.74/1.92 tff(8325,plain,
% 1.74/1.92 (~(elem!1 = z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[7116, 1, 8324])).
% 1.74/1.92 tff(8326,plain,
% 1.74/1.92 (~(z = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[445, 8325])).
% 1.74/1.92 tff(8327,plain,
% 1.74/1.92 (b(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1044, 8326, 1052])).
% 1.74/1.92 tff(8328,plain,
% 1.74/1.92 (b(elem!1, z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[545, 8325, 1050])).
% 1.74/1.92 tff(8329,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8330,plain,
% 1.74/1.92 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8331,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8330])).
% 1.74/1.93 tff(8332,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8331, 8329])).
% 1.74/1.93 tff(8333,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8334,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8333, 8332])).
% 1.74/1.93 tff(8335,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8334, 77, 360, 155, 228])).
% 1.74/1.93 tff(8336,plain,
% 1.74/1.93 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2054, 21, 8335])).
% 1.74/1.93 tff(8337,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8336, 2044])).
% 1.74/1.93 tff(8338,plain,
% 1.74/1.93 (~r(s(s(z)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4008, 156, 360])).
% 1.74/1.93 tff(8339,plain,
% 1.74/1.93 (s(s(z)) = elem!1),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[426, 8338, 1])).
% 1.74/1.93 tff(8340,plain,
% 1.74/1.93 (s(s(s(z))) = s(elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8339])).
% 1.74/1.93 tff(8341,plain,
% 1.74/1.93 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8340])).
% 1.74/1.93 tff(8342,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8341])).
% 1.74/1.93 tff(8343,plain,
% 1.74/1.93 (r(s(s(elem!1)), z)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[228, 8342])).
% 1.74/1.93 tff(8344,plain,
% 1.74/1.93 (~r(s(z), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5948, 77, 155, 8343])).
% 1.74/1.93 tff(8345,plain,
% 1.74/1.93 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[716, 21, 8344])).
% 1.74/1.93 tff(8346,plain,
% 1.74/1.93 (b(s(z), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8345, 706])).
% 1.74/1.93 tff(8347,plain,
% 1.74/1.93 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8340])).
% 1.74/1.93 tff(8348,plain,
% 1.74/1.93 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[8341])).
% 1.74/1.93 tff(8349,plain,
% 1.74/1.93 ((s(s(elem!1)) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8348])).
% 1.74/1.93 tff(8350,plain,
% 1.74/1.93 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8349, 1580])).
% 1.74/1.93 tff(8351,plain,
% 1.74/1.93 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 1.74/1.93 inference(symmetry,[status(thm)],[8350])).
% 1.74/1.93 tff(8352,plain,
% 1.74/1.93 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8351])).
% 1.74/1.93 tff(8353,plain,
% 1.74/1.93 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1362, 8352])).
% 1.74/1.93 tff(8354,plain,
% 1.74/1.93 (b(elem!1, z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2403, 8339, 8324])).
% 1.74/1.93 tff(8355,plain,
% 1.74/1.93 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8339])).
% 1.74/1.93 tff(8356,plain,
% 1.74/1.93 ((s(s(z)) = z) <=> (z = elem!1)),
% 1.74/1.93 inference(transitivity,[status(thm)],[8355, 440])).
% 1.74/1.93 tff(8357,plain,
% 1.74/1.93 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8356])).
% 1.74/1.93 tff(8358,plain,
% 1.74/1.93 (~(z = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[11, 8357])).
% 1.74/1.93 tff(8359,plain,
% 1.74/1.93 (b(z, elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1044, 8358, 1052])).
% 1.74/1.93 tff(8360,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[576])).
% 1.74/1.93 tff(8361,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[8360])).
% 1.74/1.93 tff(8362,plain,
% 1.74/1.93 (~r(s(s(s(z))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3961, 3953, 228])).
% 1.74/1.93 tff(8363,plain,
% 1.74/1.93 (b(s(s(s(z))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[63, 8362])).
% 1.74/1.93 tff(8364,plain,
% 1.74/1.93 (~b(s(s(s(z))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5560, 8363, 537, 1055])).
% 1.74/1.93 tff(8365,plain,
% 1.74/1.93 (r(s(s(s(z))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2725, 8364, 7622])).
% 1.74/1.93 tff(8366,plain,
% 1.74/1.93 (r(s(elem!1), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[647, 8365, 370])).
% 1.74/1.93 tff(8367,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[556])).
% 1.74/1.93 tff(8368,plain,
% 1.74/1.93 (r(s(s(elem!1)), z)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[228, 8367])).
% 1.74/1.93 tff(8369,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[555])).
% 1.74/1.93 tff(8370,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[8369])).
% 1.74/1.93 tff(8371,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[556, 555])).
% 1.74/1.93 tff(8372,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8371, 8370])).
% 1.74/1.93 tff(8373,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[3953, 8372])).
% 1.74/1.93 tff(8374,plain,
% 1.74/1.93 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6910, 8373, 8365])).
% 1.74/1.93 tff(8375,plain,
% 1.74/1.93 (b(s(s(elem!1)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[743, 8374, 574])).
% 1.74/1.93 tff(8376,plain,
% 1.74/1.93 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4310, 8375, 1055, 8368, 537, 913])).
% 1.74/1.93 tff(8377,plain,
% 1.74/1.93 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[885, 8376, 569])).
% 1.74/1.93 tff(8378,plain,
% 1.74/1.93 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4819, 77, 8377, 8366])).
% 1.74/1.93 tff(8379,plain,
% 1.74/1.93 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8378, 7995])).
% 1.74/1.93 tff(8380,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1380, 8379])).
% 1.74/1.93 tff(8381,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8380, 8361])).
% 1.74/1.93 tff(8382,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4053, 77, 360, 8377])).
% 1.74/1.93 tff(8383,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[870, 21, 829, 8382])).
% 1.74/1.93 tff(8384,plain,
% 1.74/1.93 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[3222])).
% 1.74/1.93 tff(8385,plain,
% 1.74/1.93 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[370])).
% 1.74/1.93 tff(8386,plain,
% 1.74/1.93 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[8385])).
% 1.74/1.93 tff(8387,plain,
% 1.74/1.93 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[593, 1743])).
% 1.74/1.93 tff(8388,plain,
% 1.74/1.93 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8387])).
% 1.74/1.93 tff(8389,plain,
% 1.74/1.93 (~(elem!1 = s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[100, 8388])).
% 1.74/1.93 tff(8390,plain,
% 1.74/1.93 (~b(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5469, 8363, 537, 1055])).
% 1.74/1.93 tff(8391,plain,
% 1.74/1.93 (r(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1345, 8390, 8389])).
% 1.74/1.93 tff(8392,plain,
% 1.74/1.93 (r(s(s(z)), s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8391, 8386])).
% 1.74/1.93 tff(8393,plain,
% 1.74/1.93 (~r(s(z), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2319, 8392, 156])).
% 1.74/1.93 tff(8394,plain,
% 1.74/1.93 (b(s(z), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[194, 8393])).
% 1.74/1.93 tff(8395,plain,
% 1.74/1.93 (b(s(z), s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8394, 8384])).
% 1.74/1.93 tff(8396,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8397,plain,
% 1.74/1.93 (((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8398,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8397])).
% 1.74/1.93 tff(8399,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8398, 8396])).
% 1.74/1.93 tff(8400,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8401,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8400, 8399])).
% 1.74/1.93 tff(8402,plain,
% 1.74/1.93 (~r(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8401, 77, 360, 8366])).
% 1.74/1.93 tff(8403,plain,
% 1.74/1.93 (b(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[735, 21, 843, 8402])).
% 1.74/1.93 tff(8404,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8405,plain,
% 1.74/1.93 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8406,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8405])).
% 1.74/1.93 tff(8407,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8406, 8404])).
% 1.74/1.93 tff(8408,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8409,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8408, 8407])).
% 1.74/1.93 tff(8410,plain,
% 1.74/1.93 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8409, 116, 8403, 8395, 8383])).
% 1.74/1.93 tff(8411,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8410, 8381])).
% 1.74/1.93 tff(8412,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(z)) = elem!1)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(elem!1)) = elem!1) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(8413,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8412, 8339, 360, 8359, 8354, 8353, 156, 228])).
% 1.74/1.93 tff(8414,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3951, 8413])).
% 1.74/1.93 tff(8415,plain,
% 1.74/1.93 (r(z, s(s(z))) <=> r(z, elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8339])).
% 1.74/1.93 tff(8416,plain,
% 1.74/1.93 (r(z, elem!1) <=> r(z, s(s(z)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[8415])).
% 1.74/1.93 tff(8417,plain,
% 1.74/1.93 ((~r(z, elem!1)) <=> (~r(z, s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8416])).
% 1.74/1.93 tff(8418,plain,
% 1.74/1.93 (~r(z, s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1052, 8417])).
% 1.74/1.93 tff(8419,plain,
% 1.74/1.93 (b(z, s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1174, 8418])).
% 1.74/1.93 tff(8420,plain,
% 1.74/1.93 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8348])).
% 1.74/1.93 tff(8421,plain,
% 1.74/1.93 ((~r(s(z), s(s(elem!1)))) <=> (~r(s(z), s(s(s(s(z))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8420])).
% 1.74/1.93 tff(8422,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8344, 8421])).
% 1.74/1.93 tff(8423,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[325, 8422])).
% 1.74/1.93 tff(8424,plain,
% 1.74/1.93 (~b(s(s(s(z))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2803, 8423, 8324, 8419, 156, 8414])).
% 1.74/1.93 tff(8425,plain,
% 1.74/1.93 (r(s(s(s(z))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[63, 8424])).
% 1.74/1.93 tff(8426,plain,
% 1.74/1.93 (r(s(elem!1), z)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8425, 8347])).
% 1.74/1.93 tff(8427,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8428,plain,
% 1.74/1.93 (((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8429,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8428])).
% 1.74/1.93 tff(8430,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8429, 8427])).
% 1.74/1.93 tff(8431,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8432,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8431, 8430])).
% 1.74/1.93 tff(8433,plain,
% 1.74/1.93 (~r(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8432, 77, 360, 155, 8426])).
% 1.74/1.93 tff(8434,plain,
% 1.74/1.93 (~(s(elem!1) = s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[842, 8339])).
% 1.74/1.93 tff(8435,plain,
% 1.74/1.93 (b(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[735, 21, 8434, 8433])).
% 1.74/1.93 tff(8436,plain,
% 1.74/1.93 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[608, 8339])).
% 1.74/1.93 tff(8437,plain,
% 1.74/1.93 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8340])).
% 1.74/1.93 tff(8438,plain,
% 1.74/1.93 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[8437])).
% 1.74/1.93 tff(8439,plain,
% 1.74/1.93 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8438])).
% 1.74/1.93 tff(8440,plain,
% 1.74/1.93 (~r(s(elem!1), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[7563, 77, 8343, 8426])).
% 1.74/1.93 tff(8441,plain,
% 1.74/1.93 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8440, 8439])).
% 1.74/1.93 tff(8442,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[664, 8441, 8436])).
% 1.74/1.93 tff(8443,plain,
% 1.74/1.93 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4150, 8442, 8339])).
% 1.74/1.93 tff(8444,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8445,plain,
% 1.74/1.93 (((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8446,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8445])).
% 1.74/1.93 tff(8447,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8446, 8444])).
% 1.74/1.93 tff(8448,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8449,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8448, 8447])).
% 1.74/1.93 tff(8450,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8449, 77, 360, 155, 8343])).
% 1.74/1.93 tff(8451,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[808, 8450])).
% 1.74/1.93 tff(8452,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8453,plain,
% 1.74/1.93 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8454,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8453])).
% 1.74/1.93 tff(8455,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8454, 8452])).
% 1.74/1.93 tff(8456,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8457,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8456, 8455])).
% 1.74/1.93 tff(8458,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8457, 116, 8451, 8443, 8435, 8346])).
% 1.74/1.93 tff(8459,plain,((~r(s(z), s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | r(z, elem!1) | (elem!1 = s(s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(8460,plain,
% 1.74/1.93 (~r(s(z), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8459, 1, 155, 228, 1052, 1362, 360])).
% 1.74/1.93 tff(8461,plain,
% 1.74/1.93 (b(s(z), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[172, 8460])).
% 1.74/1.93 tff(8462,plain,
% 1.74/1.93 (~(s(s(z)) = elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[376, 8461, 340])).
% 1.74/1.93 tff(8463,plain,
% 1.74/1.93 (r(s(s(z)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[426, 8462, 1])).
% 1.74/1.93 tff(8464,plain,
% 1.74/1.93 (~r(s(s(z)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5476, 77, 360, 8463])).
% 1.74/1.93 tff(8465,plain,
% 1.74/1.93 (b(s(s(z)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[391, 21, 388, 8464])).
% 1.74/1.93 tff(8466,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8467,plain,
% 1.74/1.93 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8468,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[8467])).
% 1.74/1.93 tff(8469,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[8468, 8466])).
% 1.74/1.93 tff(8470,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8471,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[8470, 8469])).
% 1.74/1.93 tff(8472,plain,
% 1.74/1.93 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[8471, 116, 8324, 8465, 8461, 8337])).
% 1.74/1.93 tff(8473,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[226, 8472])).
% 1.74/1.93 tff(8474,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2280, 77, 155, 228])).
% 1.74/1.93 tff(8475,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[325, 8474])).
% 1.74/1.93 tff(8476,plain,
% 1.74/1.93 (~r(s(z), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[201, 77, 155, 67])).
% 1.74/1.93 tff(8477,plain,
% 1.74/1.93 (b(s(z), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[194, 8476])).
% 1.74/1.93 tff(8478,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(8479,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(8480,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8479, 8478])).
% 1.74/1.94 tff(8481,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8480, 77, 229, 67, 228])).
% 1.74/1.94 tff(8482,plain,
% 1.74/1.94 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1146, 8481])).
% 1.74/1.94 tff(8483,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3961, 67, 228])).
% 1.74/1.94 tff(8484,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3951, 8483])).
% 1.74/1.94 tff(8485,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8486,plain,
% 1.74/1.94 (((~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(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8487,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8486])).
% 1.74/1.94 tff(8488,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[8487, 8485])).
% 1.74/1.94 tff(8489,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(8490,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8489, 8488])).
% 1.74/1.94 tff(8491,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8490, 116, 8484, 8482, 8477, 8475])).
% 1.74/1.94 tff(8492,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(8493,plain,
% 1.74/1.94 (~r(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8492, 8473, 228, 155])).
% 1.74/1.94 tff(8494,plain,
% 1.74/1.94 (b(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[63, 8493])).
% 1.74/1.94 tff(8495,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5469, 8494, 8328, 8327])).
% 1.74/1.94 tff(8496,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8497,plain,
% 1.74/1.94 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8498,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8497])).
% 1.74/1.94 tff(8499,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[8498, 8496])).
% 1.74/1.94 tff(8500,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(8501,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8500, 8499])).
% 1.74/1.94 tff(8502,plain,
% 1.74/1.94 (~b(s(s(z)), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8501, 116, 8327, 8328, 8494, 8324])).
% 1.74/1.94 tff(8503,plain,
% 1.74/1.94 (r(s(s(z)), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[105, 8502])).
% 1.74/1.94 tff(8504,plain,
% 1.74/1.94 (~r(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5025, 8503, 8463])).
% 1.74/1.94 tff(8505,plain,
% 1.74/1.94 (elem!1 = s(s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1345, 8504, 8495])).
% 1.74/1.94 tff(8506,plain,
% 1.74/1.94 (s(elem!1) = s(s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8505])).
% 1.74/1.94 tff(8507,plain,
% 1.74/1.94 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8506])).
% 1.74/1.94 tff(8508,plain,
% 1.74/1.94 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.74/1.94 inference(symmetry,[status(thm)],[8507])).
% 1.74/1.94 tff(8509,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8508])).
% 1.74/1.94 tff(8510,plain,
% 1.74/1.94 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(symmetry,[status(thm)],[8509])).
% 1.74/1.94 tff(8511,plain,
% 1.74/1.94 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8505])).
% 1.74/1.94 tff(8512,plain,
% 1.74/1.94 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(symmetry,[status(thm)],[8511])).
% 1.74/1.94 tff(8513,plain,
% 1.74/1.94 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8507])).
% 1.74/1.94 tff(8514,plain,
% 1.74/1.94 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[8513])).
% 1.74/1.94 tff(8515,plain,
% 1.74/1.94 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(transitivity,[status(thm)],[8514, 8512])).
% 1.74/1.94 tff(8516,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8517,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(8518,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8517, 8516])).
% 1.74/1.94 tff(8519,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8518, 116, 8327, 8328, 8494, 8324])).
% 1.74/1.94 tff(8520,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[89, 21, 8519, 56])).
% 1.74/1.94 tff(8521,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5905, 8520, 8473])).
% 1.74/1.94 tff(8522,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3951, 8521])).
% 1.74/1.94 tff(8523,plain,
% 1.74/1.94 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8505])).
% 1.74/1.94 tff(8524,plain,
% 1.74/1.94 (b(z, s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8327, 8523])).
% 1.74/1.94 tff(8525,plain,
% 1.74/1.94 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8506])).
% 1.74/1.94 tff(8526,plain,
% 1.74/1.94 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[8525, 1393])).
% 1.74/1.94 tff(8527,plain,
% 1.74/1.94 ((~(s(elem!1) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8526])).
% 1.74/1.94 tff(8528,plain,
% 1.74/1.94 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[3756, 8527])).
% 1.74/1.94 tff(8529,plain,
% 1.74/1.94 (~r(z, s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2549, 8473, 228])).
% 1.74/1.94 tff(8530,plain,
% 1.74/1.94 (b(z, s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1174, 8529])).
% 1.74/1.94 tff(8531,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8532,plain,
% 1.74/1.94 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8533,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8532])).
% 1.74/1.94 tff(8534,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[8533, 8531])).
% 1.74/1.94 tff(8535,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(8536,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8535, 8534])).
% 1.74/1.94 tff(8537,plain,
% 1.74/1.94 (~b(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8536, 116, 8324, 8530, 8461])).
% 1.74/1.94 tff(8538,plain,
% 1.74/1.94 (r(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[289, 8537])).
% 1.74/1.94 tff(8539,plain,
% 1.74/1.94 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5120, 116, 2247, 255, 5031])).
% 1.74/1.94 tff(8540,plain,
% 1.74/1.94 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[898, 21, 895, 8539])).
% 1.74/1.94 tff(8541,plain,
% 1.74/1.94 (~b(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2359, 116, 2247, 255, 28])).
% 1.74/1.94 tff(8542,plain,
% 1.74/1.94 (r(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1576, 21, 8541, 1563])).
% 1.74/1.94 tff(8543,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8544,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(8545,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8544, 8543])).
% 1.74/1.94 tff(8546,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)],[8545, 116, 2247, 255, 28, 5031])).
% 1.74/1.94 tff(8547,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)],[1405, 8546, 6021])).
% 1.74/1.94 tff(8548,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8549,plain,
% 1.74/1.94 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8550,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(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))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8549])).
% 1.74/1.94 tff(8551,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(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)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[8550, 8548])).
% 1.74/1.94 tff(8552,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(8553,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8552, 8551])).
% 1.74/1.94 tff(8554,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8553, 77, 293, 8547, 8542, 8540])).
% 1.74/1.94 tff(8555,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(z))) | (s(s(s(s(s(z))))) = s(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)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(8556,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)],[8555, 8538, 8528, 8494, 8524, 8522])).
% 1.74/1.94 tff(8557,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)],[1380, 8556])).
% 1.74/1.94 tff(8558,plain,
% 1.74/1.94 (r(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8557, 8515])).
% 1.74/1.94 tff(8559,plain,
% 1.74/1.94 (~r(s(s(elem!1)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1245, 8558, 360])).
% 1.74/1.94 tff(8560,plain,
% 1.74/1.94 (b(s(s(elem!1)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[808, 8559])).
% 1.74/1.94 tff(8561,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8560, 8510])).
% 1.74/1.94 tff(8562,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4997, 77, 8503, 8557])).
% 1.74/1.94 tff(8563,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 8562])).
% 1.74/1.94 tff(8564,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8565,plain,
% 1.74/1.94 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8566,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8565])).
% 1.74/1.94 tff(8567,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[8566, 8564])).
% 1.74/1.94 tff(8568,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(8569,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8568, 8567])).
% 1.74/1.94 tff(8570,plain,
% 1.74/1.94 (~b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8569, 116, 8324, 8465, 8461, 8563])).
% 1.74/1.94 tff(8571,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8570, 8561])).
% 1.74/1.94 tff(8572,plain,(b(s(s(z)), elem!1) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | r(z, elem!1) | r(elem!1, z) | b(s(z), elem!1) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(8573,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[8572, 8307, 3406, 1, 8310, 360, 340, 8308])).
% 1.74/1.94 tff(8574,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[247, 8573])).
% 1.74/1.94 tff(8575,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1063, 8574, 8311, 8309])).
% 1.74/1.94 tff(8576,plain,
% 1.74/1.94 (r(elem!1, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1068, 8575, 8307])).
% 1.74/1.94 tff(8577,plain,
% 1.74/1.94 (r(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[8576, 8303])).
% 1.74/1.94 tff(8578,plain,
% 1.74/1.94 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8284])).
% 1.74/1.94 tff(8579,plain,
% 1.74/1.94 (r(elem!1, s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[3651, 8578])).
% 1.74/1.94 tff(8580,plain,
% 1.74/1.94 (~r(s(s(elem!1)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[802, 8579, 8577])).
% 1.74/1.94 tff(8581,plain,
% 1.74/1.94 (b(s(s(elem!1)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[808, 8580])).
% 1.74/1.94 tff(8582,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8583,plain,
% 1.74/1.94 (((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(8584,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[8583])).
% 1.74/1.94 tff(8585,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8584, 8582])).
% 1.74/1.95 tff(8586,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8587,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8586, 8585])).
% 1.74/1.95 tff(8588,plain,
% 1.74/1.95 (~b(s(elem!1), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8587, 116, 8581, 8299, 8295])).
% 1.74/1.95 tff(8589,plain,
% 1.74/1.95 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4150, 8588, 8284])).
% 1.74/1.95 tff(8590,plain,
% 1.74/1.95 (r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[664, 8589, 8293])).
% 1.74/1.95 tff(8591,plain,
% 1.74/1.95 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8590, 8292])).
% 1.74/1.95 tff(8592,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8593,plain,
% 1.74/1.95 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8594,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8593])).
% 1.74/1.95 tff(8595,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8594, 8592])).
% 1.74/1.95 tff(8596,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8597,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8596, 8595])).
% 1.74/1.95 tff(8598,plain,
% 1.74/1.95 (~r(elem!1, s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8597, 77, 8577, 8591])).
% 1.74/1.95 tff(8599,plain,
% 1.74/1.95 (~r(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8598, 8291])).
% 1.74/1.95 tff(8600,plain,
% 1.74/1.95 (b(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1345, 8599, 5772])).
% 1.74/1.95 tff(8601,plain,
% 1.74/1.95 (b(elem!1, s(elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8600, 8289])).
% 1.74/1.95 tff(8602,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8300])).
% 1.74/1.95 tff(8603,plain,
% 1.74/1.95 (b(s(s(elem!1)), z)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8574, 8602])).
% 1.74/1.95 tff(8604,plain,
% 1.74/1.95 (~(s(elem!1) = elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[483, 8284])).
% 1.74/1.95 tff(8605,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8606,plain,
% 1.74/1.95 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8607,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8606])).
% 1.74/1.95 tff(8608,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8607, 8605])).
% 1.74/1.95 tff(8609,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8610,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8609, 8608])).
% 1.74/1.95 tff(8611,plain,
% 1.74/1.95 (~r(s(elem!1), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8610, 77, 8579, 8577, 8591])).
% 1.74/1.95 tff(8612,plain,
% 1.74/1.95 (b(s(elem!1), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[781, 8611, 8604])).
% 1.74/1.95 tff(8613,plain,
% 1.74/1.95 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8301])).
% 1.74/1.95 tff(8614,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(symmetry,[status(thm)],[8613])).
% 1.74/1.95 tff(8615,plain,
% 1.74/1.95 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1584, 8307])).
% 1.74/1.95 tff(8616,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8617,plain,
% 1.74/1.95 (((~b(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)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8618,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8617])).
% 1.74/1.95 tff(8619,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8618, 8616])).
% 1.74/1.95 tff(8620,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8621,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8620, 8619])).
% 1.74/1.95 tff(8622,plain,
% 1.74/1.95 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8621, 116, 8581, 8299, 8295])).
% 1.74/1.95 tff(8623,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3257, 8622, 8284])).
% 1.74/1.95 tff(8624,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3951, 8623])).
% 1.74/1.95 tff(8625,plain,
% 1.74/1.95 (~(elem!1 = s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1992, 1989, 537])).
% 1.74/1.95 tff(8626,plain,
% 1.74/1.95 (~(s(z) = elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1984, 8625])).
% 1.74/1.95 tff(8627,plain,
% 1.74/1.95 (~r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[201, 77, 3406, 67])).
% 1.74/1.95 tff(8628,plain,
% 1.74/1.95 (b(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[194, 8627])).
% 1.74/1.95 tff(8629,plain,
% 1.74/1.95 (~r(s(s(s(z))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2134, 77, 3406, 67])).
% 1.74/1.95 tff(8630,plain,
% 1.74/1.95 (b(s(s(s(z))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[402, 21, 135, 8629])).
% 1.74/1.95 tff(8631,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.74/1.95 tff(8632,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8633,plain,
% 1.74/1.95 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8634,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8633])).
% 1.74/1.95 tff(8635,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8634, 8632])).
% 1.74/1.95 tff(8636,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8637,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8636, 8635])).
% 1.74/1.95 tff(8638,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8637, 116, 847, 1332, 175, 8631])).
% 1.74/1.95 tff(8639,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(8640,plain,
% 1.74/1.95 (~b(s(z), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8639, 8630, 1332, 8628])).
% 1.74/1.95 tff(8641,plain,
% 1.74/1.95 (r(s(z), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[357, 8640, 8626])).
% 1.74/1.95 tff(8642,plain,
% 1.74/1.95 (~r(z, elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[690, 8641, 3406])).
% 1.74/1.95 tff(8643,plain,
% 1.74/1.95 (b(z, elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1044, 8642, 518])).
% 1.74/1.95 tff(8644,plain,
% 1.74/1.95 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8645,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8644])).
% 1.74/1.95 tff(8646,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8645, 2653])).
% 1.74/1.95 tff(8647,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8648,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8647, 8646])).
% 1.74/1.95 tff(8649,plain,
% 1.74/1.95 (~b(s(s(z)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8648, 116, 1055, 537, 1331])).
% 1.74/1.95 tff(8650,plain,
% 1.74/1.95 (r(s(s(z)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[25, 8649])).
% 1.74/1.95 tff(8651,plain,
% 1.74/1.95 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[96, 77, 67, 8650])).
% 1.74/1.95 tff(8652,plain,
% 1.74/1.95 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[104, 8651, 100])).
% 1.74/1.95 tff(8653,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8654,plain,
% 1.74/1.95 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8655,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8654])).
% 1.74/1.95 tff(8656,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8655, 8653])).
% 1.74/1.95 tff(8657,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8658,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8657, 8656])).
% 1.74/1.95 tff(8659,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8658, 116, 1332, 8652, 1331, 175, 8631])).
% 1.74/1.95 tff(8660,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(8661,plain,
% 1.74/1.95 (~b(s(s(z)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8660, 8628, 1332, 8630, 67, 8643, 537])).
% 1.74/1.95 tff(8662,plain,
% 1.74/1.95 (~r(s(s(z)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5526, 8641, 2418, 3953])).
% 1.74/1.95 tff(8663,plain,
% 1.74/1.95 (s(s(z)) = elem!1),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[426, 8662, 8661])).
% 1.74/1.95 tff(8664,plain,
% 1.74/1.95 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[568, 8663])).
% 1.74/1.95 tff(8665,plain,
% 1.74/1.95 (s(s(s(z))) = s(elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8663])).
% 1.74/1.95 tff(8666,plain,
% 1.74/1.95 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8665])).
% 1.74/1.95 tff(8667,plain,
% 1.74/1.95 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[8666])).
% 1.74/1.95 tff(8668,plain,
% 1.74/1.95 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8667])).
% 1.74/1.95 tff(8669,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(symmetry,[status(thm)],[8668])).
% 1.74/1.95 tff(8670,plain,
% 1.74/1.95 (r(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2418, 8669])).
% 1.74/1.95 tff(8671,plain,
% 1.74/1.95 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8666])).
% 1.74/1.95 tff(8672,plain,
% 1.74/1.95 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5499, 77, 8641, 3953, 2418])).
% 1.74/1.95 tff(8673,plain,
% 1.74/1.95 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[323, 21, 320, 8672])).
% 1.74/1.95 tff(8674,plain,
% 1.74/1.95 (b(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8673, 8671])).
% 1.74/1.95 tff(8675,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8666])).
% 1.74/1.95 tff(8676,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8677,plain,
% 1.74/1.95 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(8678,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8677])).
% 1.74/1.95 tff(8679,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[8678, 8676])).
% 1.74/1.95 tff(8680,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(8681,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8680, 8679])).
% 1.74/1.95 tff(8682,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8681, 77, 8641, 2418])).
% 1.74/1.95 tff(8683,plain,
% 1.74/1.95 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2054, 21, 8682])).
% 1.74/1.95 tff(8684,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[8683, 2044])).
% 1.74/1.95 tff(8685,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[8684, 8675])).
% 1.74/1.95 tff(8686,plain,
% 1.74/1.95 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4610, 8685, 8674, 8663, 8670, 8641])).
% 1.74/1.95 tff(8687,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[885, 8686, 8664])).
% 1.74/1.95 tff(8688,plain,
% 1.74/1.95 (~(s(elem!1) = elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[483, 8663])).
% 1.74/1.95 tff(8689,plain,
% 1.74/1.95 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[8665, 8666])).
% 1.74/1.96 tff(8690,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8691,plain,
% 1.74/1.96 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8692,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8691])).
% 1.74/1.96 tff(8693,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8692, 8690])).
% 1.74/1.96 tff(8694,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(8695,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8694, 8693])).
% 1.74/1.96 tff(8696,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8695, 116, 8628, 8630, 8684])).
% 1.74/1.96 tff(8697,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1145, 8696, 1141])).
% 1.74/1.96 tff(8698,plain,
% 1.74/1.96 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8697, 8689])).
% 1.74/1.96 tff(8699,plain,
% 1.74/1.96 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[529, 8663, 518])).
% 1.74/1.96 tff(8700,plain,
% 1.74/1.96 (~(elem!1 = s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2182, 8699])).
% 1.74/1.96 tff(8701,plain,
% 1.74/1.96 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8667])).
% 1.74/1.96 tff(8702,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8701])).
% 1.74/1.96 tff(8703,plain,
% 1.74/1.96 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8702])).
% 1.74/1.96 tff(8704,plain,
% 1.74/1.96 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1063, 8643, 254, 537])).
% 1.74/1.96 tff(8705,plain,
% 1.74/1.96 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8704, 8703])).
% 1.74/1.96 tff(8706,plain,
% 1.74/1.96 (r(elem!1, s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1892, 8705, 8700])).
% 1.74/1.96 tff(8707,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8708,plain,
% 1.74/1.96 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8709,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8708])).
% 1.74/1.96 tff(8710,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8709, 8707])).
% 1.74/1.96 tff(8711,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(8712,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8711, 8710])).
% 1.74/1.96 tff(8713,plain,
% 1.74/1.96 (~r(s(elem!1), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8712, 77, 8706, 8698])).
% 1.74/1.96 tff(8714,plain,
% 1.74/1.96 (b(s(elem!1), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[781, 8713, 8688])).
% 1.74/1.96 tff(8715,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8716,plain,
% 1.74/1.96 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8717,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8716])).
% 1.74/1.96 tff(8718,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8717, 8715])).
% 1.74/1.96 tff(8719,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(8720,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8719, 8718])).
% 1.74/1.96 tff(8721,plain,
% 1.74/1.96 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8720, 116, 8643, 537, 8714, 8687])).
% 1.74/1.96 tff(8722,plain,
% 1.74/1.96 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[836, 8663, 8699])).
% 1.74/1.96 tff(8723,plain,
% 1.74/1.96 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[858, 21, 8722, 8721])).
% 1.74/1.96 tff(8724,plain,
% 1.74/1.96 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4300, 116, 8643, 537, 8687])).
% 1.74/1.96 tff(8725,plain,
% 1.74/1.96 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[898, 21, 895, 8724])).
% 1.74/1.96 tff(8726,plain,
% 1.74/1.96 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8665])).
% 1.74/1.96 tff(8727,plain,
% 1.74/1.96 (r(s(elem!1), z)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[67, 8726])).
% 1.74/1.96 tff(8728,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4643, 77, 8727, 8725, 8723])).
% 1.74/1.96 tff(8729,plain,(b(s(z), z) | (~b(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), z)) | (z = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(8730,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8729, 8600, 67, 1989, 8280, 8624, 8311, 8574])).
% 1.74/1.96 tff(8731,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1596, 8730, 8615])).
% 1.74/1.96 tff(8732,plain,
% 1.74/1.96 (b(s(s(elem!1)), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8731, 8614])).
% 1.74/1.96 tff(8733,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8734,plain,
% 1.74/1.96 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8735,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8734])).
% 1.74/1.96 tff(8736,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8735, 8733])).
% 1.74/1.96 tff(8737,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(8738,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8737, 8736])).
% 1.74/1.96 tff(8739,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8738, 116, 8309, 8732, 8612, 8603, 8601])).
% 1.74/1.96 tff(8740,plain,((~r(s(z), elem!1)) | (~r(s(s(s(z))), z)) | b(s(z), z) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | b(s(s(z)), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(8741,plain,
% 1.74/1.96 (~r(s(z), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8740, 1989, 67, 175, 3651, 1, 340])).
% 1.74/1.96 tff(8742,plain,
% 1.74/1.96 (s(z) = elem!1),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[357, 8741, 340])).
% 1.74/1.96 tff(8743,plain,
% 1.74/1.96 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1531, 8742])).
% 1.74/1.96 tff(8744,plain,
% 1.74/1.96 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1584, 8743])).
% 1.74/1.96 tff(8745,plain,
% 1.74/1.96 (s(s(z)) = s(elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8742])).
% 1.74/1.96 tff(8746,plain,
% 1.74/1.96 (s(elem!1) = s(s(z))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8745])).
% 1.74/1.96 tff(8747,plain,
% 1.74/1.96 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8746])).
% 1.74/1.96 tff(8748,plain,
% 1.74/1.96 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8747])).
% 1.74/1.96 tff(8749,plain,
% 1.74/1.96 (~(s(s(z)) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[480, 8742])).
% 1.74/1.96 tff(8750,plain,
% 1.74/1.96 (~(elem!1 = s(s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8749, 7134])).
% 1.74/1.96 tff(8751,plain,
% 1.74/1.96 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.96 tff(8752,plain,
% 1.74/1.96 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8751])).
% 1.74/1.96 tff(8753,plain,
% 1.74/1.96 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8752])).
% 1.74/1.96 tff(8754,plain,
% 1.74/1.96 (s(s(s(z))) = s(s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.96 tff(8755,plain,
% 1.74/1.96 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8754])).
% 1.74/1.96 tff(8756,plain,
% 1.74/1.96 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8755])).
% 1.74/1.96 tff(8757,plain,
% 1.74/1.96 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8756])).
% 1.74/1.96 tff(8758,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.96 tff(8759,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8758, 8757])).
% 1.74/1.96 tff(8760,plain,
% 1.74/1.96 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8754])).
% 1.74/1.96 tff(8761,plain,
% 1.74/1.96 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8742])).
% 1.74/1.96 tff(8762,plain,
% 1.74/1.96 (b(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[175, 8761])).
% 1.74/1.96 tff(8763,plain,
% 1.74/1.96 (b(elem!1, s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8762, 8760])).
% 1.74/1.96 tff(8764,plain,
% 1.74/1.96 (r(s(s(z)), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[426, 8749, 1])).
% 1.74/1.96 tff(8765,plain,
% 1.74/1.96 (elem!1 = s(z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1984, 8742])).
% 1.74/1.96 tff(8766,plain,
% 1.74/1.96 (~b(elem!1, z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1992, 8765, 1989])).
% 1.74/1.96 tff(8767,plain,
% 1.74/1.96 (r(elem!1, z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[545, 8766, 8279])).
% 1.74/1.96 tff(8768,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8754])).
% 1.74/1.96 tff(8769,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8742])).
% 1.74/1.96 tff(8770,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8298, 8769])).
% 1.74/1.96 tff(8771,plain,
% 1.74/1.96 (b(s(s(elem!1)), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8770, 8768])).
% 1.74/1.96 tff(8772,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2650, 228, 575])).
% 1.74/1.96 tff(8773,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1596, 8772, 1585])).
% 1.74/1.96 tff(8774,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3961, 228, 67])).
% 1.74/1.96 tff(8775,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3951, 8774])).
% 1.74/1.96 tff(8776,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2016, 8775, 466])).
% 1.74/1.96 tff(8777,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3455, 116, 616, 1879, 8776, 8773])).
% 1.74/1.96 tff(8778,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(8779,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8778, 8771, 8763, 8742, 8767, 67])).
% 1.74/1.96 tff(8780,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[247, 8779])).
% 1.74/1.96 tff(8781,plain,
% 1.74/1.96 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1474])).
% 1.74/1.96 tff(8782,plain,
% 1.74/1.96 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8781])).
% 1.74/1.96 tff(8783,plain,
% 1.74/1.96 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8782])).
% 1.74/1.96 tff(8784,plain,
% 1.74/1.96 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1474])).
% 1.74/1.96 tff(8785,plain,
% 1.74/1.96 (b(s(elem!1), z)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[7113, 8784])).
% 1.74/1.96 tff(8786,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8787,plain,
% 1.74/1.96 (((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8788,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8787])).
% 1.74/1.96 tff(8789,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8788, 8786])).
% 1.74/1.96 tff(8790,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(8791,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8790, 8789])).
% 1.74/1.96 tff(8792,plain,
% 1.74/1.96 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8791, 116, 1055, 1879, 8785, 254])).
% 1.74/1.96 tff(8793,plain,
% 1.74/1.96 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8792, 8783])).
% 1.74/1.96 tff(8794,plain,
% 1.74/1.96 (r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[149, 8793])).
% 1.74/1.96 tff(8795,plain,
% 1.74/1.96 (r(s(elem!1), s(s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8794, 1521])).
% 1.74/1.96 tff(8796,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1474])).
% 1.74/1.96 tff(8797,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[8796])).
% 1.74/1.96 tff(8798,plain,
% 1.74/1.96 ((~b(s(s(s(s(z)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8797])).
% 1.74/1.96 tff(8799,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8800,plain,
% 1.74/1.96 (((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8801,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8800])).
% 1.74/1.96 tff(8802,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8801, 8799])).
% 1.74/1.96 tff(8803,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(8804,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8803, 8802])).
% 1.74/1.96 tff(8805,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8804, 116, 1055, 1879, 8785, 254])).
% 1.74/1.96 tff(8806,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8805, 8798])).
% 1.74/1.96 tff(8807,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[226, 8806])).
% 1.74/1.96 tff(8808,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8807, 4253])).
% 1.74/1.96 tff(8809,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1542, 8794, 466, 428])).
% 1.74/1.96 tff(8810,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4128, 8809, 1055, 254])).
% 1.74/1.96 tff(8811,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1596, 8810, 1585])).
% 1.74/1.96 tff(8812,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8813,plain,
% 1.74/1.96 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(8814,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[8813])).
% 1.74/1.96 tff(8815,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[8814, 8812])).
% 1.74/1.96 tff(8816,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(8817,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[8816, 8815])).
% 1.74/1.96 tff(8818,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[8817, 77, 8811, 1524, 8808, 8795])).
% 1.74/1.96 tff(8819,plain,((~b(z, elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(8820,plain,
% 1.74/1.97 (~b(z, elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8819, 8742, 8780, 8764, 8763])).
% 1.74/1.97 tff(8821,plain,
% 1.74/1.97 (~b(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[7603, 8820, 8742])).
% 1.74/1.97 tff(8822,plain,
% 1.74/1.97 (r(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[289, 8821])).
% 1.74/1.97 tff(8823,plain,
% 1.74/1.97 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8746])).
% 1.74/1.97 tff(8824,plain,
% 1.74/1.97 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.74/1.97 inference(symmetry,[status(thm)],[8823])).
% 1.74/1.97 tff(8825,plain,
% 1.74/1.97 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.97 tff(8826,plain,
% 1.74/1.97 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[8825])).
% 1.74/1.97 tff(8827,plain,
% 1.74/1.97 ((~r(z, s(elem!1))) <=> (~r(z, s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8826])).
% 1.74/1.97 tff(8828,plain,
% 1.74/1.97 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.97 tff(8829,plain,
% 1.74/1.97 (r(s(elem!1), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8764, 8828])).
% 1.74/1.97 tff(8830,plain,
% 1.74/1.97 (r(z, elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1044, 8820, 8280])).
% 1.74/1.97 tff(8831,plain,
% 1.74/1.97 (~r(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8141, 8830, 8829])).
% 1.74/1.97 tff(8832,plain,
% 1.74/1.97 (~r(z, s(s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8831, 8827])).
% 1.74/1.97 tff(8833,plain,
% 1.74/1.97 (b(z, s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1174, 8832])).
% 1.74/1.97 tff(8834,plain,
% 1.74/1.97 (b(z, s(elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8833, 8824])).
% 1.74/1.97 tff(8835,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.74/1.97 tff(8836,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2136, 155, 67])).
% 1.74/1.97 tff(8837,plain,
% 1.74/1.97 (b(s(s(s(z))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[402, 21, 135, 8836])).
% 1.74/1.97 tff(8838,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8839,plain,
% 1.74/1.97 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8840,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8839])).
% 1.74/1.97 tff(8841,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[8840, 8838])).
% 1.74/1.97 tff(8842,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(8843,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8842, 8841])).
% 1.74/1.97 tff(8844,plain,
% 1.74/1.97 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8843, 116, 28, 175, 8837])).
% 1.74/1.97 tff(8845,plain,
% 1.74/1.97 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[325, 8844])).
% 1.74/1.97 tff(8846,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8847,plain,
% 1.74/1.97 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8848,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8847])).
% 1.74/1.97 tff(8849,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[8848, 8846])).
% 1.74/1.97 tff(8850,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(8851,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8850, 8849])).
% 1.74/1.97 tff(8852,plain,
% 1.74/1.97 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8851, 116, 28, 175, 8837])).
% 1.74/1.97 tff(8853,plain,
% 1.74/1.97 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2054, 21, 8852])).
% 1.74/1.97 tff(8854,plain,
% 1.74/1.97 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8853, 2044])).
% 1.74/1.97 tff(8855,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8856,plain,
% 1.74/1.97 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8857,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8856])).
% 1.74/1.97 tff(8858,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[8857, 8855])).
% 1.74/1.97 tff(8859,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(8860,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8859, 8858])).
% 1.74/1.97 tff(8861,plain,
% 1.74/1.97 (~r(z, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8860, 77, 293, 8854])).
% 1.74/1.97 tff(8862,plain,
% 1.74/1.97 (b(z, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1576, 21, 8861, 1563])).
% 1.74/1.97 tff(8863,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2280, 77, 155, 228, 327])).
% 1.74/1.97 tff(8864,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(8865,plain,
% 1.74/1.97 (~r(s(s(s(s(z)))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8864, 8845, 155])).
% 1.74/1.97 tff(8866,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[247, 8865])).
% 1.74/1.97 tff(8867,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8868,plain,
% 1.74/1.97 (((~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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(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)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8869,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8868])).
% 1.74/1.97 tff(8870,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[8869, 8867])).
% 1.74/1.97 tff(8871,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(8872,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8871, 8870])).
% 1.74/1.97 tff(8873,plain,
% 1.74/1.97 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8872, 116, 1303, 28, 8866, 8862])).
% 1.74/1.97 tff(8874,plain,
% 1.74/1.97 (r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[149, 8873])).
% 1.74/1.97 tff(8875,plain,
% 1.74/1.97 (~r(s(z), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[336, 8874, 8845])).
% 1.74/1.97 tff(8876,plain,
% 1.74/1.97 (b(s(z), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[172, 8875])).
% 1.74/1.97 tff(8877,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8878,plain,
% 1.74/1.97 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8879,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8878])).
% 1.74/1.97 tff(8880,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[8879, 8877])).
% 1.74/1.97 tff(8881,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(8882,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8881, 8880])).
% 1.74/1.97 tff(8883,plain,
% 1.74/1.97 (~r(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8882, 77, 155, 8874, 8845])).
% 1.74/1.97 tff(8884,plain,
% 1.74/1.97 (b(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[391, 21, 388, 8883])).
% 1.74/1.97 tff(8885,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8886,plain,
% 1.74/1.97 (((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8887,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[8886])).
% 1.74/1.97 tff(8888,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[8887, 8885])).
% 1.74/1.97 tff(8889,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(8890,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[8889, 8888])).
% 1.74/1.97 tff(8891,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[8890, 116, 1303, 8884, 8876, 8837])).
% 1.74/1.97 tff(8892,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[89, 21, 8891, 56])).
% 1.74/1.97 tff(8893,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8894,plain,
% 1.74/1.97 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(8895,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8894])).
% 1.74/1.98 tff(8896,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8895, 8893])).
% 1.74/1.98 tff(8897,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8898,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8897, 8896])).
% 1.74/1.98 tff(8899,plain,
% 1.74/1.98 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8898, 116, 1303, 28, 8866, 8862])).
% 1.74/1.98 tff(8900,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[226, 8899])).
% 1.74/1.98 tff(8901,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8902,plain,
% 1.74/1.98 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8903,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8902])).
% 1.74/1.98 tff(8904,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8903, 8901])).
% 1.74/1.98 tff(8905,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8906,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8905, 8904])).
% 1.74/1.98 tff(8907,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8906, 77, 8900, 8892])).
% 1.74/1.98 tff(8908,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1146, 8907])).
% 1.74/1.98 tff(8909,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.98 tff(8910,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(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(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8911,plain,
% 1.74/1.98 (((~b(s(s(s(z))), s(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(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(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(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8912,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8911])).
% 1.74/1.98 tff(8913,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8912, 8910])).
% 1.74/1.98 tff(8914,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8915,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8914, 8913])).
% 1.74/1.98 tff(8916,plain,
% 1.74/1.98 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8915, 116, 28, 1177, 8909, 1176])).
% 1.74/1.98 tff(8917,plain,
% 1.74/1.98 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[898, 21, 895, 8916])).
% 1.74/1.98 tff(8918,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8919,plain,
% 1.74/1.98 (((~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(z, s(s(s(s(z)))))) | (~b(z, 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(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8920,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8919])).
% 1.74/1.98 tff(8921,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8920, 8918])).
% 1.74/1.98 tff(8922,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8923,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8922, 8921])).
% 1.74/1.98 tff(8924,plain,
% 1.74/1.98 (~b(z, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8923, 116, 28, 1177, 1176])).
% 1.74/1.98 tff(8925,plain,
% 1.74/1.98 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[267, 21, 8924])).
% 1.74/1.98 tff(8926,plain,
% 1.74/1.98 (r(z, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8925, 253])).
% 1.74/1.98 tff(8927,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8928,plain,
% 1.74/1.98 (((~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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8929,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8928])).
% 1.74/1.98 tff(8930,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8929, 8927])).
% 1.74/1.98 tff(8931,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8932,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8931, 8930])).
% 1.74/1.98 tff(8933,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)],[8932, 116, 28, 1177, 8909])).
% 1.74/1.98 tff(8934,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)],[1380, 8933])).
% 1.74/1.98 tff(8935,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8936,plain,
% 1.74/1.98 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8937,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8936])).
% 1.74/1.98 tff(8938,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8937, 8935])).
% 1.74/1.98 tff(8939,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8940,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8939, 8938])).
% 1.74/1.98 tff(8941,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8940, 77, 293, 8934, 8926, 8917])).
% 1.74/1.98 tff(8942,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(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))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(8943,plain,
% 1.74/1.98 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8942, 8908, 28, 293, 8862])).
% 1.74/1.98 tff(8944,plain,
% 1.74/1.98 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6694, 8943])).
% 1.74/1.98 tff(8945,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(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(8946,plain,
% 1.74/1.98 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(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(8947,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8946])).
% 1.74/1.98 tff(8948,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8947, 8945])).
% 1.74/1.98 tff(8949,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8950,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(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))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8949, 8948])).
% 1.74/1.98 tff(8951,plain,
% 1.74/1.98 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8950, 77, 8944, 8845])).
% 1.74/1.98 tff(8952,plain,
% 1.74/1.98 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[870, 21, 1901, 8951])).
% 1.74/1.98 tff(8953,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8954,plain,
% 1.74/1.98 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(s(z))))), 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(8955,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8954])).
% 1.74/1.98 tff(8956,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8955, 8953])).
% 1.74/1.98 tff(8957,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(8958,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[8957, 8956])).
% 1.74/1.98 tff(8959,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[8958, 77, 2235, 8874, 8944])).
% 1.74/1.98 tff(8960,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 8959])).
% 1.74/1.98 tff(8961,plain,
% 1.74/1.98 (~r(z, s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7618, 8892, 67])).
% 1.74/1.98 tff(8962,plain,
% 1.74/1.98 (b(z, s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1174, 8961])).
% 1.74/1.98 tff(8963,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8964,plain,
% 1.74/1.98 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(8965,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[8964])).
% 1.74/1.98 tff(8966,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[8965, 8963])).
% 1.74/1.98 tff(8967,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(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(8968,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8967, 8966])).
% 1.74/1.99 tff(8969,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[8968, 116, 1303, 8962, 8876, 8960, 8952])).
% 1.74/1.99 tff(8970,plain,((~r(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(8971,plain,
% 1.74/1.99 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[8970, 2235, 67, 293, 7113, 175, 155])).
% 1.74/1.99 tff(8972,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3951, 8971])).
% 1.74/1.99 tff(8973,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3961, 8972, 67])).
% 1.74/1.99 tff(8974,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[247, 8973])).
% 1.74/1.99 tff(8975,plain,
% 1.74/1.99 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1476])).
% 1.74/1.99 tff(8976,plain,
% 1.74/1.99 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.99 inference(symmetry,[status(thm)],[8975])).
% 1.74/1.99 tff(8977,plain,
% 1.74/1.99 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1474])).
% 1.74/1.99 tff(8978,plain,
% 1.74/1.99 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[8977, 8976])).
% 1.74/1.99 tff(8979,plain,
% 1.74/1.99 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2235, 8978])).
% 1.74/1.99 tff(8980,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8972, 4328])).
% 1.74/1.99 tff(8981,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(8982,plain,
% 1.74/1.99 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(8983,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[8982])).
% 1.74/1.99 tff(8984,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[8983, 8981])).
% 1.74/1.99 tff(8985,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(8986,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8985, 8984])).
% 1.74/1.99 tff(8987,plain,
% 1.74/1.99 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[8986, 77, 8980, 8979])).
% 1.74/1.99 tff(8988,plain,
% 1.74/1.99 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8987, 5654])).
% 1.74/1.99 tff(8989,plain,
% 1.74/1.99 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[149, 8988])).
% 1.74/1.99 tff(8990,plain,
% 1.74/1.99 (b(s(elem!1), s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8989, 8781])).
% 1.74/1.99 tff(8991,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(8992,plain,
% 1.74/1.99 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(8993,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[8992])).
% 1.74/1.99 tff(8994,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[8993, 8991])).
% 1.74/1.99 tff(8995,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(8996,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8995, 8994])).
% 1.74/1.99 tff(8997,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[8996, 77, 8980, 8979])).
% 1.74/1.99 tff(8998,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8997, 5669])).
% 1.74/1.99 tff(8999,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[226, 8998])).
% 1.74/1.99 tff(9000,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[8999, 8796])).
% 1.74/1.99 tff(9001,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9002,plain,
% 1.74/1.99 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9003,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9002])).
% 1.74/1.99 tff(9004,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))), s(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9003, 9001])).
% 1.74/1.99 tff(9005,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9006,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9005, 9004])).
% 1.74/1.99 tff(9007,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9006, 116, 9000, 8990, 8974, 8835])).
% 1.74/1.99 tff(9008,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(z, s(elem!1))) | (~(s(z) = elem!1)) | (~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9009,plain,
% 1.74/1.99 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9008, 8834, 8742, 67, 8822, 175, 3406])).
% 1.74/1.99 tff(9010,plain,
% 1.74/1.99 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[105, 9009])).
% 1.74/1.99 tff(9011,plain,
% 1.74/1.99 (b(s(elem!1), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9010, 8759])).
% 1.74/1.99 tff(9012,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9013,plain,
% 1.74/1.99 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9014,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9013])).
% 1.74/1.99 tff(9015,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9014, 9012])).
% 1.74/1.99 tff(9016,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9017,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9016, 9015])).
% 1.74/1.99 tff(9018,plain,
% 1.74/1.99 (~b(elem!1, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9017, 116, 8771, 8763, 9011])).
% 1.74/1.99 tff(9019,plain,
% 1.74/1.99 (~b(elem!1, s(s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9018, 8753])).
% 1.74/1.99 tff(9020,plain,
% 1.74/1.99 (r(elem!1, s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6497, 9019, 8750])).
% 1.74/1.99 tff(9021,plain,
% 1.74/1.99 (r(elem!1, s(elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9020, 8748])).
% 1.74/1.99 tff(9022,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[8746])).
% 1.74/1.99 tff(9023,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(symmetry,[status(thm)],[9022])).
% 1.74/1.99 tff(9024,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.99 tff(9025,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(symmetry,[status(thm)],[9024])).
% 1.74/1.99 tff(9026,plain,
% 1.74/1.99 ((~b(s(s(s(s(z)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9025])).
% 1.74/1.99 tff(9027,plain,
% 1.74/1.99 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[8745])).
% 1.74/1.99 tff(9028,plain,
% 1.74/1.99 (b(s(elem!1), z)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7113, 9027])).
% 1.74/1.99 tff(9029,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9030,plain,
% 1.74/1.99 (((~b(s(elem!1), 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)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9031,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9030])).
% 1.74/1.99 tff(9032,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9031, 9029])).
% 1.74/1.99 tff(9033,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9034,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9033, 9032])).
% 1.74/1.99 tff(9035,plain,
% 1.74/1.99 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9034, 116, 9028, 8780, 8834])).
% 1.74/1.99 tff(9036,plain,
% 1.74/1.99 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9035, 9026])).
% 1.74/1.99 tff(9037,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[226, 9036])).
% 1.74/1.99 tff(9038,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9037, 9023])).
% 1.74/1.99 tff(9039,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9040,plain,
% 1.74/1.99 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9041,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9040])).
% 1.74/1.99 tff(9042,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9041, 9039])).
% 1.74/1.99 tff(9043,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9044,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9043, 9042])).
% 1.74/1.99 tff(9045,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9044, 77, 9038, 9021])).
% 1.74/1.99 tff(9046,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1596, 9045, 8744])).
% 1.74/1.99 tff(9047,plain,
% 1.74/1.99 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[8742])).
% 1.74/1.99 tff(9048,plain,
% 1.74/1.99 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.99 inference(transitivity,[status(thm)],[9047, 4222])).
% 1.74/1.99 tff(9049,plain,
% 1.74/1.99 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9048])).
% 1.74/1.99 tff(9050,plain,
% 1.74/1.99 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[1901, 9049])).
% 1.74/1.99 tff(9051,plain,
% 1.74/1.99 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1364, 8743])).
% 1.74/1.99 tff(9052,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9053,plain,
% 1.74/1.99 (((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(9054,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[9053])).
% 1.74/1.99 tff(9055,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[9054, 9052])).
% 1.74/1.99 tff(9056,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(9057,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[9056, 9055])).
% 1.74/1.99 tff(9058,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9057, 116, 2844, 1031, 8835, 7382])).
% 1.74/1.99 tff(9059,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(9060,plain,
% 1.74/1.99 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[9059, 8834, 8830, 9051, 9028, 8829])).
% 1.74/1.99 tff(9061,plain,
% 1.74/1.99 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[885, 9060, 9050])).
% 1.74/1.99 tff(9062,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4862, 9046, 9061, 8770, 8762])).
% 1.74/2.00 tff(9063,plain,
% 1.74/2.00 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3951, 9062])).
% 1.74/2.00 tff(9064,plain,
% 1.74/2.00 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2016, 9063, 8742])).
% 1.74/2.00 tff(9065,plain,
% 1.74/2.00 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9066,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9065])).
% 1.74/2.00 tff(9067,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9066, 3450])).
% 1.74/2.00 tff(9068,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9069,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9068, 9067])).
% 1.74/2.00 tff(9070,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9069, 116, 8771, 8763, 9064, 9046])).
% 1.74/2.00 tff(9071,plain,(b(s(z), z) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | b(s(s(z)), elem!1) | b(s(z), elem!1) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9072,plain,
% 1.74/2.00 (b(s(z), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9071, 67, 175, 1, 340, 3651])).
% 1.74/2.00 tff(9073,plain,
% 1.74/2.00 (b(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[8215, 9072, 340, 3651, 1])).
% 1.74/2.00 tff(9074,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[7993])).
% 1.74/2.00 tff(9075,plain,
% 1.74/2.00 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9074])).
% 1.74/2.00 tff(9076,plain,
% 1.74/2.00 (~r(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3295, 448, 360])).
% 1.74/2.00 tff(9077,plain,
% 1.74/2.00 (b(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[289, 9076])).
% 1.74/2.00 tff(9078,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7649, 9077, 448, 270, 360])).
% 1.74/2.00 tff(9079,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[885, 9078, 569])).
% 1.74/2.00 tff(9080,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.74/2.00 tff(9081,plain,
% 1.74/2.00 (~r(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9080, 7607])).
% 1.74/2.00 tff(9082,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[638, 9081])).
% 1.74/2.00 tff(9083,plain,((~r(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(s(z))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9084,plain,
% 1.74/2.00 (~r(s(s(s(z))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9083, 7619, 370])).
% 1.74/2.00 tff(9085,plain,
% 1.74/2.00 (~r(s(elem!1), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9084, 615])).
% 1.74/2.00 tff(9086,plain,
% 1.74/2.00 (b(s(elem!1), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[681, 21, 570, 9085])).
% 1.74/2.00 tff(9087,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9088,plain,
% 1.74/2.00 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9089,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9088])).
% 1.74/2.00 tff(9090,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9089, 9087])).
% 1.74/2.00 tff(9091,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9092,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9091, 9090])).
% 1.74/2.00 tff(9093,plain,
% 1.74/2.00 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9092, 116, 537, 9077, 9086, 9079])).
% 1.74/2.00 tff(9094,plain,
% 1.74/2.00 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9093, 9075])).
% 1.74/2.00 tff(9095,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[557])).
% 1.74/2.00 tff(9096,plain,
% 1.74/2.00 ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9095])).
% 1.74/2.00 tff(9097,plain,
% 1.74/2.00 (~r(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1446, 448, 360, 270])).
% 1.74/2.00 tff(9098,plain,
% 1.74/2.00 (b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[743, 9097, 574])).
% 1.74/2.00 tff(9099,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9100,plain,
% 1.74/2.00 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9101,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9100])).
% 1.74/2.00 tff(9102,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9101, 9099])).
% 1.74/2.00 tff(9103,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9104,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9103, 9102])).
% 1.74/2.00 tff(9105,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9104, 116, 537, 9098, 9077, 9079])).
% 1.74/2.00 tff(9106,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9105, 9096])).
% 1.74/2.00 tff(9107,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9108,plain,
% 1.74/2.00 (((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9109,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9108])).
% 1.74/2.00 tff(9110,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9109, 9107])).
% 1.74/2.00 tff(9111,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9112,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9111, 9110])).
% 1.74/2.00 tff(9113,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9112, 116, 537, 9098, 9077, 9086])).
% 1.74/2.00 tff(9114,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3257, 9113, 370])).
% 1.74/2.00 tff(9115,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3951, 9114])).
% 1.74/2.00 tff(9116,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4691, 9115, 9106])).
% 1.74/2.00 tff(9117,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9116, 9094])).
% 1.74/2.00 tff(9118,plain,((~r(z, elem!1)) | (~(s(s(z)) = elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9119,plain,
% 1.74/2.00 (~r(z, elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9118, 8284, 9073, 67, 9072, 360, 8285])).
% 1.74/2.00 tff(9120,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[370])).
% 1.74/2.00 tff(9121,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[9120])).
% 1.74/2.00 tff(9122,plain,
% 1.74/2.00 (~(s(s(elem!1)) = elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[529, 370, 8280])).
% 1.74/2.00 tff(9123,plain,
% 1.74/2.00 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[836, 370, 9122])).
% 1.74/2.00 tff(9124,plain,
% 1.74/2.00 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[8306, 9123])).
% 1.74/2.00 tff(9125,plain,
% 1.74/2.00 (b(z, elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1044, 1052, 8280])).
% 1.74/2.00 tff(9126,plain,
% 1.74/2.00 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1063, 254, 537, 9125])).
% 1.74/2.00 tff(9127,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1068, 9126, 9124])).
% 1.74/2.00 tff(9128,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9127, 9121])).
% 1.74/2.00 tff(9129,plain,
% 1.74/2.00 (~b(s(z), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[376, 370, 340])).
% 1.74/2.00 tff(9130,plain,
% 1.74/2.00 (r(s(z), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[172, 9129])).
% 1.74/2.00 tff(9131,plain,
% 1.74/2.00 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7968, 254, 270, 340, 1, 9130, 1052])).
% 1.74/2.00 tff(9132,plain,
% 1.74/2.00 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[325, 9131])).
% 1.74/2.00 tff(9133,plain,
% 1.74/2.00 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[336, 9132, 9130])).
% 1.74/2.00 tff(9134,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9133, 9128])).
% 1.74/2.00 tff(9135,plain,((~b(s(s(s(s(z)))), z)) | (~(s(s(z)) = elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | b(s(z), elem!1) | b(s(s(z)), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9136,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9135, 8284, 9073, 9072, 340, 1, 9119])).
% 1.74/2.00 tff(9137,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[247, 9136])).
% 1.74/2.00 tff(9138,plain,
% 1.74/2.00 (b(z, elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1044, 9119, 8280])).
% 1.74/2.00 tff(9139,plain,
% 1.74/2.00 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3961, 9137, 67])).
% 1.74/2.00 tff(9140,plain,
% 1.74/2.00 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3951, 9139])).
% 1.74/2.00 tff(9141,plain,
% 1.74/2.00 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[555])).
% 1.74/2.00 tff(9142,plain,
% 1.74/2.00 (b(s(z), s(elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[175, 9141])).
% 1.74/2.00 tff(9143,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[556])).
% 1.74/2.00 tff(9144,plain,
% 1.74/2.00 (b(s(z), s(s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[249, 9143])).
% 1.74/2.00 tff(9145,plain,
% 1.74/2.00 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[555])).
% 1.74/2.00 tff(9146,plain,
% 1.74/2.00 (r(s(elem!1), z)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[67, 9145])).
% 1.74/2.00 tff(9147,plain,
% 1.74/2.00 (~r(s(elem!1), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7563, 77, 8368, 9146])).
% 1.74/2.00 tff(9148,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9147, 7557])).
% 1.74/2.00 tff(9149,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[664, 9148, 609])).
% 1.74/2.00 tff(9150,plain,
% 1.74/2.00 (b(s(elem!1), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4150, 9149, 370])).
% 1.74/2.00 tff(9151,plain,
% 1.74/2.00 (r(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[357, 481, 340])).
% 1.74/2.00 tff(9152,plain,
% 1.74/2.00 (~(s(s(elem!1)) = elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[529, 370, 7422])).
% 1.74/2.00 tff(9153,plain,
% 1.74/2.00 (b(s(s(z)), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6088, 340])).
% 1.74/2.00 tff(9154,plain,
% 1.74/2.00 (b(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2403, 370, 9153])).
% 1.74/2.00 tff(9155,plain,
% 1.74/2.00 (~r(s(elem!1), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7563, 77, 3208, 5326])).
% 1.74/2.00 tff(9156,plain,
% 1.74/2.00 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9155, 7557])).
% 1.74/2.00 tff(9157,plain,
% 1.74/2.00 (b(s(s(s(z))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[664, 9156, 609])).
% 1.74/2.00 tff(9158,plain,
% 1.74/2.00 (b(s(elem!1), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4150, 9157, 370])).
% 1.74/2.00 tff(9159,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9160,plain,
% 1.74/2.00 (((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9161,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9160])).
% 1.74/2.00 tff(9162,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9161, 9159])).
% 1.74/2.00 tff(9163,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(9164,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[9163, 9162])).
% 1.74/2.00 tff(9165,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9164, 116, 537, 616, 9158, 4602, 4055])).
% 1.74/2.00 tff(9166,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~(s(s(z)) = elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(9167,plain,
% 1.74/2.00 (~b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[9166, 9154, 9144, 9142, 370, 8368, 9146])).
% 1.74/2.00 tff(9168,plain,
% 1.74/2.00 (r(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[743, 9167, 9152])).
% 1.74/2.00 tff(9169,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1245, 9168, 9151])).
% 1.74/2.00 tff(9170,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[808, 9169])).
% 1.74/2.00 tff(9171,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9172,plain,
% 1.74/2.00 (((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(9173,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[9172])).
% 1.74/2.00 tff(9174,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[9173, 9171])).
% 1.74/2.01 tff(9175,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9176,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9175, 9174])).
% 1.74/2.01 tff(9177,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9176, 116, 9170, 270, 9150, 9144, 9142])).
% 1.74/2.01 tff(9178,plain,((~(s(s(z)) = elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(9179,plain,
% 1.74/2.01 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9178, 370, 270, 228, 175, 67, 340])).
% 1.74/2.01 tff(9180,plain,
% 1.74/2.01 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[325, 9179])).
% 1.74/2.01 tff(9181,plain,
% 1.74/2.01 (r(s(z), s(s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9180, 7929])).
% 1.74/2.01 tff(9182,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3257, 370, 28])).
% 1.74/2.01 tff(9183,plain,
% 1.74/2.01 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[836, 370, 9152])).
% 1.74/2.01 tff(9184,plain,
% 1.74/2.01 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4310, 616, 1055, 913, 537, 3208])).
% 1.74/2.01 tff(9185,plain,
% 1.74/2.01 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[885, 9184, 569])).
% 1.74/2.01 tff(9186,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9187,plain,
% 1.74/2.01 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9188,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9187])).
% 1.74/2.01 tff(9189,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[9188, 9186])).
% 1.74/2.01 tff(9190,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9191,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9190, 9189])).
% 1.74/2.01 tff(9192,plain,
% 1.74/2.01 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9191, 77, 360, 9185])).
% 1.74/2.01 tff(9193,plain,
% 1.74/2.01 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5816, 21, 9192])).
% 1.74/2.01 tff(9194,plain,
% 1.74/2.01 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9193, 5783])).
% 1.74/2.01 tff(9195,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9196,plain,
% 1.74/2.01 (((~b(z, elem!1)) | (~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))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9197,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9196])).
% 1.74/2.01 tff(9198,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[9197, 9195])).
% 1.74/2.01 tff(9199,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9200,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9199, 9198])).
% 1.74/2.01 tff(9201,plain,
% 1.74/2.01 (~b(s(s(s(s(s(z))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9200, 116, 1055, 270, 271, 9194])).
% 1.74/2.01 tff(9202,plain,
% 1.74/2.01 (r(s(s(s(s(s(z))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[898, 21, 895, 9201])).
% 1.74/2.01 tff(9203,plain,
% 1.74/2.01 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4643, 77, 5326, 9202])).
% 1.74/2.01 tff(9204,plain,
% 1.74/2.01 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[858, 21, 855, 9203])).
% 1.74/2.01 tff(9205,plain,
% 1.74/2.01 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4308, 77, 3208, 9202])).
% 1.74/2.01 tff(9206,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[916, 21, 913, 9205])).
% 1.74/2.01 tff(9207,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9208,plain,
% 1.74/2.01 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9209,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9208])).
% 1.74/2.01 tff(9210,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[9209, 9207])).
% 1.74/2.01 tff(9211,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9212,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9211, 9210])).
% 1.74/2.01 tff(9213,plain,
% 1.74/2.01 (~b(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9212, 116, 616, 9158, 1877, 4055])).
% 1.74/2.01 tff(9214,plain,
% 1.74/2.01 (r(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[808, 9213])).
% 1.74/2.01 tff(9215,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9216,plain,
% 1.74/2.01 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9217,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9216])).
% 1.74/2.01 tff(9218,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[9217, 9215])).
% 1.74/2.01 tff(9219,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9220,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9219, 9218])).
% 1.74/2.01 tff(9221,plain,
% 1.74/2.01 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9220, 77, 9214, 3208, 9202])).
% 1.74/2.01 tff(9222,plain,
% 1.74/2.01 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9221, 4591])).
% 1.74/2.01 tff(9223,plain,
% 1.74/2.01 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6694, 9222])).
% 1.74/2.01 tff(9224,plain,
% 1.74/2.01 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9223, 4585])).
% 1.74/2.01 tff(9225,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9226,plain,
% 1.74/2.01 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9227,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9226])).
% 1.74/2.01 tff(9228,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[9227, 9225])).
% 1.74/2.01 tff(9229,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9230,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9229, 9228])).
% 1.74/2.01 tff(9231,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9230, 116, 616, 9158, 9224, 9206, 9204])).
% 1.74/2.01 tff(9232,plain,((~b(s(s(elem!1)), elem!1)) | (~(s(s(z)) = elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(9233,plain,
% 1.74/2.01 (~b(s(s(elem!1)), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9232, 370, 9183, 8368, 9146, 9182, 9142, 1055, 270, 271, 9151, 9154])).
% 1.74/2.01 tff(9234,plain,
% 1.74/2.01 (r(s(s(elem!1)), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[743, 9233, 9152])).
% 1.74/2.01 tff(9235,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9236,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9237,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9236, 9235])).
% 1.74/2.01 tff(9238,plain,
% 1.74/2.01 (~r(s(z), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9237, 77, 9234, 9151, 8368])).
% 1.74/2.01 tff(9239,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9238, 9181])).
% 1.74/2.01 tff(9240,plain,((~(s(s(z)) = elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(9241,plain,
% 1.74/2.01 (~b(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9240, 9140, 175, 9138, 9072, 8284, 67, 340, 9137])).
% 1.74/2.01 tff(9242,plain,
% 1.74/2.01 (~b(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[376, 8284, 340])).
% 1.74/2.01 tff(9243,plain,
% 1.74/2.01 (r(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[172, 9242])).
% 1.74/2.01 tff(9244,plain,
% 1.74/2.01 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9178, 9137, 175, 8284, 9072, 67, 340])).
% 1.74/2.01 tff(9245,plain,
% 1.74/2.01 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[325, 9244])).
% 1.74/2.01 tff(9246,plain,
% 1.74/2.01 (~r(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7959, 9245, 9138, 8285, 360, 8284, 9243])).
% 1.74/2.01 tff(9247,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[289, 9246, 9241])).
% 1.74/2.01 tff(9248,plain,((~r(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | b(s(z), elem!1) | b(s(s(z)), elem!1) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(9249,plain,
% 1.74/2.01 (~r(s(z), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9248, 64, 8278, 340, 1, 7120])).
% 1.74/2.01 tff(9250,plain,
% 1.74/2.01 (s(z) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[357, 9249, 340])).
% 1.74/2.01 tff(9251,plain,
% 1.74/2.01 (s(s(z)) = s(elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9250])).
% 1.74/2.01 tff(9252,plain,
% 1.74/2.01 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9251])).
% 1.74/2.01 tff(9253,plain,
% 1.74/2.01 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9251])).
% 1.74/2.01 tff(9254,plain,
% 1.74/2.01 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.74/2.01 inference(symmetry,[status(thm)],[9253])).
% 1.74/2.01 tff(9255,plain,
% 1.74/2.01 ((~r(z, s(elem!1))) <=> (~r(z, s(s(z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9254])).
% 1.74/2.01 tff(9256,plain,
% 1.74/2.01 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9251])).
% 1.74/2.01 tff(9257,plain,
% 1.74/2.01 (~(s(s(z)) = elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[480, 9250])).
% 1.74/2.01 tff(9258,plain,
% 1.74/2.01 (r(s(s(z)), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[426, 9257, 1])).
% 1.74/2.01 tff(9259,plain,
% 1.74/2.01 (r(s(elem!1), elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9258, 9256])).
% 1.74/2.01 tff(9260,plain,
% 1.74/2.01 (b(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9071, 64, 8278, 1, 340, 7120])).
% 1.74/2.01 tff(9261,plain,
% 1.74/2.01 (b(elem!1, z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[8215, 9260, 340, 7120, 1])).
% 1.74/2.01 tff(9262,plain,
% 1.74/2.01 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 1.74/2.01 inference(symmetry,[status(thm)],[5154])).
% 1.74/2.01 tff(9263,plain,
% 1.74/2.01 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 1.74/2.01 inference(symmetry,[status(thm)],[5153])).
% 1.74/2.01 tff(9264,plain,
% 1.74/2.01 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[9263, 9262])).
% 1.74/2.01 tff(9265,plain,
% 1.74/2.01 ((~b(elem!1, s(elem!1))) <=> (~b(s(z), s(s(z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9264])).
% 1.74/2.01 tff(9266,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9267,plain,
% 1.74/2.01 (((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(9268,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[9267])).
% 1.74/2.01 tff(9269,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[9268, 9266])).
% 1.74/2.01 tff(9270,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(9271,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9270, 9269])).
% 1.74/2.01 tff(9272,plain,
% 1.74/2.01 (~b(elem!1, s(elem!1))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[9271, 116, 5634, 537, 8785])).
% 1.74/2.01 tff(9273,plain,
% 1.74/2.01 (~b(s(z), s(s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[9272, 9265])).
% 1.74/2.01 tff(9274,plain,
% 1.74/2.01 (b(elem!1, s(s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[8278, 5631])).
% 1.74/2.02 tff(9275,plain,
% 1.74/2.02 (b(elem!1, s(s(elem!1)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9274, 5630])).
% 1.74/2.02 tff(9276,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[8819, 5634, 466, 428, 9275])).
% 1.74/2.02 tff(9277,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[247, 9276])).
% 1.74/2.02 tff(9278,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3961, 9277, 64])).
% 1.74/2.02 tff(9279,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3951, 9278])).
% 1.74/2.02 tff(9280,plain,
% 1.74/2.02 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[466])).
% 1.74/2.02 tff(9281,plain,
% 1.74/2.02 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 1.74/2.02 inference(symmetry,[status(thm)],[9280])).
% 1.74/2.02 tff(9282,plain,
% 1.74/2.02 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9281])).
% 1.74/2.02 tff(9283,plain,
% 1.74/2.02 (~b(elem!1, s(z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[3544, 9282])).
% 1.74/2.02 tff(9284,plain,
% 1.74/2.02 (r(s(s(z)), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[391, 21, 4432, 388])).
% 1.74/2.02 tff(9285,plain,
% 1.74/2.02 (~r(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7144, 271, 9153, 2235])).
% 1.74/2.02 tff(9286,plain,
% 1.74/2.02 (b(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[194, 9285])).
% 1.74/2.02 tff(9287,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[8864, 155, 8845])).
% 1.74/2.02 tff(9288,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[247, 9287])).
% 1.74/2.02 tff(9289,plain,
% 1.74/2.02 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[336, 8845, 156])).
% 1.74/2.02 tff(9290,plain,
% 1.74/2.02 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[149, 9289])).
% 1.74/2.02 tff(9291,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9292,plain,
% 1.74/2.02 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9293,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9292])).
% 1.74/2.02 tff(9294,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[9293, 9291])).
% 1.74/2.02 tff(9295,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(9296,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9295, 9294])).
% 1.74/2.02 tff(9297,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9296, 116, 271, 1303, 9290, 9288, 175])).
% 1.74/2.02 tff(9298,plain,((~r(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9299,plain,
% 1.74/2.02 (~r(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9298, 156, 9153, 9286, 271, 28, 64])).
% 1.74/2.02 tff(9300,plain,
% 1.74/2.02 (b(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[210, 9299])).
% 1.74/2.02 tff(9301,plain,
% 1.74/2.02 (~(elem!1 = s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3980, 9286, 340])).
% 1.74/2.02 tff(9302,plain,
% 1.74/2.02 (~(elem!1 = z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[409, 9300, 340])).
% 1.74/2.02 tff(9303,plain,
% 1.74/2.02 (~(z = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[445, 9302])).
% 1.74/2.02 tff(9304,plain,
% 1.74/2.02 (b(z, elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1044, 9303, 1052])).
% 1.74/2.02 tff(9305,plain,
% 1.74/2.02 (r(s(s(z)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[426, 422, 1])).
% 1.74/2.02 tff(9306,plain,
% 1.74/2.02 (~r(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4008, 9305, 156])).
% 1.74/2.02 tff(9307,plain,
% 1.74/2.02 (s(z) = elem!1),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[357, 9306, 340])).
% 1.74/2.02 tff(9308,plain,
% 1.74/2.02 (s(s(z)) = s(elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9307])).
% 1.74/2.02 tff(9309,plain,
% 1.74/2.02 (s(s(s(z))) = s(s(elem!1))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9308])).
% 1.74/2.02 tff(9310,plain,
% 1.74/2.02 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9309])).
% 1.74/2.02 tff(9311,plain,
% 1.74/2.02 ((~b(s(s(s(z))), z)) <=> (~b(s(s(elem!1)), z))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9310])).
% 1.74/2.02 tff(9312,plain,
% 1.74/2.02 (~b(s(s(elem!1)), z)),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[57, 9311])).
% 1.74/2.02 tff(9313,plain,
% 1.74/2.02 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9309])).
% 1.74/2.02 tff(9314,plain,
% 1.74/2.02 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9313])).
% 1.74/2.02 tff(9315,plain,
% 1.74/2.02 (~r(s(s(s(z))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4976, 9305, 2235])).
% 1.74/2.02 tff(9316,plain,
% 1.74/2.02 (~r(s(s(elem!1)), elem!1)),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9315, 9314])).
% 1.74/2.02 tff(9317,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7408, 9316, 9312, 9153, 270, 1055, 422])).
% 1.74/2.02 tff(9318,plain,((s(s(z)) = elem!1) | (~b(s(z), z)) | (~b(z, elem!1)) | b(s(s(s(z))), z) | b(s(z), elem!1) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9319,plain,
% 1.74/2.02 (b(s(s(z)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9318, 422, 1055, 57, 340, 2235, 156, 270])).
% 1.74/2.02 tff(9320,plain,
% 1.74/2.02 (~(s(z) = elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4434, 9319, 4432])).
% 1.74/2.02 tff(9321,plain,
% 1.74/2.02 (~r(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2824, 9319, 9153, 1055, 9320, 1620, 422, 340])).
% 1.74/2.02 tff(9322,plain,
% 1.74/2.02 (b(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[545, 9321, 7421])).
% 1.74/2.02 tff(9323,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[8648, 116, 1055, 9322, 9153, 9319])).
% 1.74/2.02 tff(9324,plain,((s(s(z)) = elem!1) | (~b(z, elem!1)) | (elem!1 = s(s(s(z)))) | b(s(z), elem!1) | b(s(s(z)), s(z)) | b(s(s(s(z))), z) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9325,plain,
% 1.74/2.02 (s(s(z)) = elem!1),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9324, 9304, 9301, 340, 4432, 57, 2235, 156, 9300])).
% 1.74/2.02 tff(9326,plain,
% 1.74/2.02 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9325])).
% 1.74/2.02 tff(9327,plain,
% 1.74/2.02 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.02 inference(symmetry,[status(thm)],[9326])).
% 1.74/2.02 tff(9328,plain,
% 1.74/2.02 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9327])).
% 1.74/2.02 tff(9329,plain,
% 1.74/2.02 (b(elem!1, z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2403, 9325, 9153])).
% 1.74/2.02 tff(9330,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9240, 9325, 9300, 271, 9304, 9286, 64, 340, 28])).
% 1.74/2.02 tff(9331,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[247, 9330])).
% 1.74/2.02 tff(9332,plain,
% 1.74/2.02 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1063, 9331, 9329, 9304])).
% 1.74/2.02 tff(9333,plain,
% 1.74/2.02 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9332, 9328])).
% 1.74/2.02 tff(9334,plain,
% 1.74/2.02 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[279, 9331, 271, 9300])).
% 1.74/2.02 tff(9335,plain,
% 1.74/2.02 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[325, 9334])).
% 1.74/2.02 tff(9336,plain,
% 1.74/2.02 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[336, 9335, 156])).
% 1.74/2.02 tff(9337,plain,
% 1.74/2.02 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[149, 9336])).
% 1.74/2.02 tff(9338,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9337, 9333])).
% 1.74/2.02 tff(9339,plain,((~r(s(z), s(s(z)))) | (~b(z, s(z))) | b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), s(z)) | b(s(s(s(z))), z) | (~r(s(s(z)), s(s(s(z))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9340,plain,
% 1.74/2.02 (~r(s(z), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9339, 4432, 340, 28, 271, 57, 2235, 1052])).
% 1.74/2.02 tff(9341,plain,
% 1.74/2.02 (b(s(z), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[172, 9340])).
% 1.74/2.02 tff(9342,plain,
% 1.74/2.02 (((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9343,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9342])).
% 1.74/2.02 tff(9344,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[9343, 8531])).
% 1.74/2.02 tff(9345,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(9346,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9345, 9344])).
% 1.74/2.02 tff(9347,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9346, 116, 271, 1303, 2442, 174])).
% 1.74/2.02 tff(9348,plain,((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9349,plain,
% 1.74/2.02 (~b(z, s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9348, 9341, 9153, 271])).
% 1.74/2.02 tff(9350,plain,
% 1.74/2.02 (r(z, s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1174, 9349])).
% 1.74/2.02 tff(9351,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2479, 77, 2235, 1212, 291])).
% 1.74/2.02 tff(9352,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9353,plain,
% 1.74/2.02 (~r(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9352, 9350, 2235])).
% 1.74/2.02 tff(9354,plain,
% 1.74/2.02 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[267, 21, 9353])).
% 1.74/2.02 tff(9355,plain,
% 1.74/2.02 (b(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9354, 253])).
% 1.74/2.02 tff(9356,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9357,plain,
% 1.74/2.02 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9358,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9357])).
% 1.74/2.02 tff(9359,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[9358, 9356])).
% 1.74/2.02 tff(9360,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(9361,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9360, 9359])).
% 1.74/2.02 tff(9362,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9361, 116, 271, 255, 175, 8631])).
% 1.74/2.02 tff(9363,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9364,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9363, 9355, 271, 9286])).
% 1.74/2.02 tff(9365,plain,
% 1.74/2.02 (r(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[402, 21, 135, 9364])).
% 1.74/2.02 tff(9366,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9367,plain,
% 1.74/2.02 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9368,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[9367])).
% 1.74/2.02 tff(9369,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[9368, 9366])).
% 1.74/2.02 tff(9370,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(9371,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9370, 9369])).
% 1.74/2.02 tff(9372,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9371, 77, 2235, 9365, 9284])).
% 1.74/2.02 tff(9373,plain,(b(s(s(z)), s(z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9374,plain,
% 1.74/2.02 (b(s(s(z)), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9373, 271, 2235, 340, 28, 57, 1052])).
% 1.74/2.02 tff(9375,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(9376,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(9377,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[9376, 9375])).
% 1.74/2.02 tff(9378,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9377, 116, 271, 1303, 175, 1048, 8631])).
% 1.74/2.02 tff(9379,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9380,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9379, 271, 9153, 9286, 9374])).
% 1.74/2.02 tff(9381,plain,
% 1.74/2.02 (r(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[402, 21, 135, 9380])).
% 1.74/2.02 tff(9382,plain,
% 1.74/2.02 (~r(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2136, 9381, 64])).
% 1.74/2.02 tff(9383,plain,
% 1.74/2.02 (b(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[210, 9382])).
% 1.74/2.02 tff(9384,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2698, 116, 9383, 271, 9153, 9374])).
% 1.74/2.02 tff(9385,plain,((~b(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(9386,plain,
% 1.74/2.02 (~b(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[9385, 57, 340, 28, 2235, 1052])).
% 1.74/2.02 tff(9387,plain,
% 1.74/2.02 (~r(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7122, 292, 67])).
% 1.86/2.02 tff(9388,plain,
% 1.86/2.02 (b(s(z), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[210, 9387])).
% 1.86/2.02 tff(9389,plain,
% 1.86/2.02 (~(elem!1 = z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[409, 9388, 340])).
% 1.86/2.02 tff(9390,plain,
% 1.86/2.02 (r(z, s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[289, 4794])).
% 1.86/2.02 tff(9391,plain,
% 1.86/2.02 (~(z = elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[445, 9389])).
% 1.86/2.02 tff(9392,plain,
% 1.86/2.02 (b(z, elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[1044, 9391, 1052])).
% 1.86/2.02 tff(9393,plain,
% 1.86/2.02 (~(s(z) = elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[4796, 9392, 4794])).
% 1.86/2.02 tff(9394,plain,
% 1.86/2.02 (~(elem!1 = s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[420, 9393])).
% 1.86/2.02 tff(9395,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(9396,plain,
% 1.86/2.02 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(9397,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[9396])).
% 1.86/2.02 tff(9398,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.02 inference(transitivity,[status(thm)],[9397, 9395])).
% 1.86/2.02 tff(9399,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(9400,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[9399, 9398])).
% 1.86/2.02 tff(9401,plain,
% 1.86/2.02 ($false),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[9400, 116, 1055, 270, 667, 1303, 1048])).
% 1.86/2.02 tff(9402,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.02 tff(9403,plain,
% 1.86/2.02 (~b(elem!1, s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[9402, 9392, 9388, 9153, 2329])).
% 1.86/2.02 tff(9404,plain,
% 1.86/2.02 (r(elem!1, s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[633, 9403, 9394])).
% 1.86/2.02 tff(9405,plain,
% 1.86/2.02 (~r(elem!1, z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2095, 9404, 9390])).
% 1.86/2.02 tff(9406,plain,
% 1.86/2.02 (b(elem!1, z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[545, 9405, 9389])).
% 1.86/2.02 tff(9407,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(9408,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(9409,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[9408, 9407])).
% 1.86/2.02 tff(9410,plain,
% 1.86/2.02 ($false),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[9409, 116, 9392, 9406, 9388, 9153, 2329])).
% 1.86/2.02 tff(9411,plain,((~r(s(z), s(s(s(z))))) | b(z, s(z)) | r(z, elem!1) | b(s(z), elem!1) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.02 tff(9412,plain,
% 1.86/2.02 (~r(s(z), s(s(s(z))))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[9411, 9386, 1052, 340, 64, 2235])).
% 1.86/2.02 tff(9413,plain,
% 1.86/2.02 (b(s(z), s(s(s(z))))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[194, 9412])).
% 1.86/2.02 tff(9414,plain,
% 1.86/2.02 (r(z, s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[289, 9386])).
% 1.86/2.02 tff(9415,plain,
% 1.86/2.02 (~r(s(z), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[8970, 9414, 2235, 28, 9153, 64, 9413])).
% 1.86/2.02 tff(9416,plain,
% 1.86/2.02 (b(s(z), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[210, 9415])).
% 1.86/2.02 tff(9417,plain,
% 1.86/2.02 (~(elem!1 = z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[409, 9416, 340])).
% 1.86/2.02 tff(9418,plain,
% 1.86/2.02 (~(z = elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[445, 9417])).
% 1.86/2.02 tff(9419,plain,
% 1.86/2.02 (b(z, elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[1044, 9418, 1052])).
% 1.86/2.02 tff(9420,plain,
% 1.86/2.02 (~(s(z) = elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[4796, 9419, 9386])).
% 1.86/2.02 tff(9421,plain,
% 1.86/2.02 (~(elem!1 = s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[420, 9420])).
% 1.86/2.02 tff(9422,plain,
% 1.86/2.02 (r(s(z), elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[357, 9420, 340])).
% 1.86/2.02 tff(9423,plain,
% 1.86/2.02 (~(s(s(z)) = elem!1)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2403, 1455, 9153])).
% 1.86/2.02 tff(9424,plain,
% 1.86/2.02 (~r(s(z), s(s(z)))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[9324, 9423, 1620, 340, 1055, 57, 2235, 4432, 270])).
% 1.86/2.02 tff(9425,plain,
% 1.86/2.02 (b(s(z), s(s(z)))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[172, 9424])).
% 1.86/2.02 tff(9426,plain,
% 1.86/2.02 (r(elem!1, z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[545, 1455, 7421])).
% 1.86/2.02 tff(9427,plain,
% 1.86/2.02 (~r(elem!1, s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[2095, 9426, 293])).
% 1.86/2.02 tff(9428,plain,
% 1.86/2.02 (b(elem!1, s(z))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[633, 9427, 1046])).
% 1.86/2.02 tff(9429,plain,
% 1.86/2.02 ($false),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[7222, 116, 1055, 270, 9428, 9153, 9425])).
% 1.86/2.02 tff(9430,plain,(b(elem!1, z) | (~b(z, elem!1)) | (~b(s(z), z)) | (elem!1 = s(z)) | (~r(z, s(z))) | (elem!1 = s(s(s(z)))) | b(s(z), elem!1) | b(s(s(s(z))), z) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(9431,plain,
% 1.86/2.03 (b(elem!1, z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9430, 4432, 270, 1046, 293, 5772, 340, 57, 2235, 1055])).
% 1.86/2.03 tff(9432,plain,
% 1.86/2.03 (~b(s(z), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7321, 116, 1055, 9431, 270, 9153])).
% 1.86/2.03 tff(9433,plain,
% 1.86/2.03 (r(s(z), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[172, 9432])).
% 1.86/2.03 tff(9434,plain,
% 1.86/2.03 (s(s(z)) = elem!1),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9324, 9433, 5772, 340, 1055, 57, 2235, 4432, 270])).
% 1.86/2.03 tff(9435,plain,
% 1.86/2.03 (~(s(s(elem!1)) = elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[529, 9434, 7422])).
% 1.86/2.03 tff(9436,plain,
% 1.86/2.03 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7959, 9435, 293, 1055, 360, 9434, 9433])).
% 1.86/2.03 tff(9437,plain,
% 1.86/2.03 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[325, 9436])).
% 1.86/2.03 tff(9438,plain,
% 1.86/2.03 (~r(s(s(s(s(z)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9178, 9437, 270, 9434, 175, 64, 340])).
% 1.86/2.03 tff(9439,plain,
% 1.86/2.03 (~b(s(s(s(s(z)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4732, 9437, 270, 1055, 9431])).
% 1.86/2.03 tff(9440,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[247, 9439, 9438])).
% 1.86/2.03 tff(9441,plain,(b(s(s(z)), s(z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | b(s(z), elem!1) | (~r(z, s(z))) | (~r(s(z), elem!1)) | b(s(s(s(z))), z) | (~r(s(s(z)), s(s(s(z))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(9442,plain,
% 1.86/2.03 (b(s(s(z)), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9441, 9416, 9419, 9413, 340, 9414, 9422, 57, 2235, 9421])).
% 1.86/2.03 tff(9443,plain,
% 1.86/2.03 (~b(elem!1, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9402, 9442, 9416, 9153, 9419])).
% 1.86/2.03 tff(9444,plain,
% 1.86/2.03 (r(elem!1, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[633, 9443, 9421])).
% 1.86/2.03 tff(9445,plain,
% 1.86/2.03 (~r(elem!1, z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2095, 9444, 9414])).
% 1.86/2.03 tff(9446,plain,
% 1.86/2.03 (b(elem!1, z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[545, 9445, 9417])).
% 1.86/2.03 tff(9447,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9409, 116, 9419, 9446, 9416, 9153, 9442])).
% 1.86/2.03 tff(9448,plain,(b(s(s(s(z))), z) | b(s(z), elem!1) | (~r(s(s(z)), s(s(s(z))))) | r(z, elem!1) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(9449,plain,
% 1.86/2.03 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9448, 9279, 340, 57, 1052])).
% 1.86/2.03 tff(9450,plain,
% 1.86/2.03 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[105, 9449])).
% 1.86/2.03 tff(9451,plain,
% 1.86/2.03 (~r(s(z), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7509, 9450, 270, 4432, 2845, 57, 9283, 5634, 340, 9279])).
% 1.86/2.03 tff(9452,plain,
% 1.86/2.03 (b(s(z), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[172, 9451])).
% 1.86/2.03 tff(9453,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9452, 9273])).
% 1.86/2.03 tff(9454,plain,(r(z, elem!1) | (~(s(z) = elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | b(s(s(z)), s(z)) | b(s(s(s(z))), z) | b(s(z), elem!1) | (~r(s(s(z)), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(9455,plain,
% 1.86/2.03 (r(z, elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9454, 9250, 9261, 9260, 4432, 57, 340, 9258, 8280])).
% 1.86/2.03 tff(9456,plain,
% 1.86/2.03 (~r(z, s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[8141, 9455, 9259])).
% 1.86/2.03 tff(9457,plain,
% 1.86/2.03 (~r(z, s(s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9456, 9255])).
% 1.86/2.03 tff(9458,plain,
% 1.86/2.03 (b(z, s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1174, 9457])).
% 1.86/2.03 tff(9459,plain,
% 1.86/2.03 (b(z, s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9458, 9252])).
% 1.86/2.03 tff(9460,plain,
% 1.86/2.03 (s(s(s(z))) = s(s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9251])).
% 1.86/2.03 tff(9461,plain,
% 1.86/2.03 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9460])).
% 1.86/2.03 tff(9462,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9460])).
% 1.86/2.03 tff(9463,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[9462])).
% 1.86/2.03 tff(9464,plain,
% 1.86/2.03 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9463])).
% 1.86/2.03 tff(9465,plain,
% 1.86/2.03 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9250])).
% 1.86/2.03 tff(9466,plain,
% 1.86/2.03 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.03 inference(transitivity,[status(thm)],[9465, 4222])).
% 1.86/2.03 tff(9467,plain,
% 1.86/2.03 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9466])).
% 1.86/2.03 tff(9468,plain,
% 1.86/2.03 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[1901, 9467])).
% 1.86/2.03 tff(9469,plain,
% 1.86/2.03 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9250])).
% 1.86/2.03 tff(9470,plain,
% 1.86/2.03 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 1.86/2.03 inference(symmetry,[status(thm)],[9469])).
% 1.86/2.03 tff(9471,plain,
% 1.86/2.03 (s(elem!1) = s(s(z))),
% 1.86/2.03 inference(symmetry,[status(thm)],[9251])).
% 1.86/2.03 tff(9472,plain,
% 1.86/2.03 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9471])).
% 1.86/2.03 tff(9473,plain,
% 1.86/2.03 ((s(s(z)) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.86/2.03 inference(symmetry,[status(thm)],[9472])).
% 1.86/2.03 tff(9474,plain,
% 1.86/2.03 ((s(s(z)) = elem!1) <=> (s(elem!1) = s(z))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9473, 9470])).
% 1.86/2.03 tff(9475,plain,
% 1.86/2.03 ((~(s(s(z)) = elem!1)) <=> (~(s(elem!1) = s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9474])).
% 1.86/2.03 tff(9476,plain,
% 1.86/2.03 (~(s(elem!1) = s(z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9257, 9475])).
% 1.86/2.03 tff(9477,plain,
% 1.86/2.03 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1531, 9250])).
% 1.86/2.03 tff(9478,plain,
% 1.86/2.03 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1364, 9477])).
% 1.86/2.03 tff(9479,plain,
% 1.86/2.03 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9251])).
% 1.86/2.03 tff(9480,plain,
% 1.86/2.03 (b(s(elem!1), z)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7113, 9479])).
% 1.86/2.03 tff(9481,plain,
% 1.86/2.03 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[6919, 9455, 9260, 9480, 9478, 9476])).
% 1.86/2.03 tff(9482,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[885, 9481, 9468])).
% 1.86/2.03 tff(9483,plain,
% 1.86/2.03 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9250])).
% 1.86/2.03 tff(9484,plain,
% 1.86/2.03 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9483])).
% 1.86/2.03 tff(9485,plain,
% 1.86/2.03 (~(s(s(elem!1)) = elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[566, 9484])).
% 1.86/2.03 tff(9486,plain,
% 1.86/2.03 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9251])).
% 1.86/2.03 tff(9487,plain,
% 1.86/2.03 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9486, 1820])).
% 1.86/2.03 tff(9488,plain,
% 1.86/2.03 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9487])).
% 1.86/2.03 tff(9489,plain,
% 1.86/2.03 (~(s(s(z)) = s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5269, 8280])).
% 1.86/2.03 tff(9490,plain,
% 1.86/2.03 (~(s(s(elem!1)) = s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9489, 9488])).
% 1.86/2.03 tff(9491,plain,
% 1.86/2.03 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9460])).
% 1.86/2.03 tff(9492,plain,
% 1.86/2.03 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9250])).
% 1.86/2.03 tff(9493,plain,
% 1.86/2.03 (b(elem!1, s(s(s(z))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[8278, 9492])).
% 1.86/2.03 tff(9494,plain,
% 1.86/2.03 (b(elem!1, s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9493, 9491])).
% 1.86/2.03 tff(9495,plain,
% 1.86/2.03 (~r(s(s(elem!1)), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2865, 752, 466, 428])).
% 1.86/2.03 tff(9496,plain,
% 1.86/2.03 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[767, 9495, 760])).
% 1.86/2.03 tff(9497,plain,
% 1.86/2.03 (~r(z, s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3440, 752, 448])).
% 1.86/2.03 tff(9498,plain,
% 1.86/2.03 (b(z, s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[514, 9497])).
% 1.86/2.03 tff(9499,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9500,plain,
% 1.86/2.03 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9501,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9500])).
% 1.86/2.03 tff(9502,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9501, 9499])).
% 1.86/2.03 tff(9503,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(9504,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9503, 9502])).
% 1.86/2.03 tff(9505,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9504, 116, 537, 668, 1879, 2844, 1877])).
% 1.86/2.03 tff(9506,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(9507,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9506, 9498, 9496, 537, 8785, 1879])).
% 1.86/2.03 tff(9508,plain,((~r(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~r(z, elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(9509,plain,
% 1.86/2.03 (~r(s(s(elem!1)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9508, 9261, 9494, 9490, 9455, 9250, 9258])).
% 1.86/2.03 tff(9510,plain,
% 1.86/2.03 (b(s(s(elem!1)), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[743, 9509, 9485])).
% 1.86/2.03 tff(9511,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9512,plain,
% 1.86/2.03 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9513,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9512])).
% 1.86/2.03 tff(9514,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9513, 9511])).
% 1.86/2.03 tff(9515,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(9516,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9515, 9514])).
% 1.86/2.03 tff(9517,plain,
% 1.86/2.03 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9516, 116, 9261, 9510, 9482, 9459])).
% 1.86/2.03 tff(9518,plain,
% 1.86/2.03 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9517, 9464])).
% 1.86/2.03 tff(9519,plain,
% 1.86/2.03 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1380, 9518])).
% 1.86/2.03 tff(9520,plain,
% 1.86/2.03 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9519, 9461])).
% 1.86/2.03 tff(9521,plain,
% 1.86/2.03 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9460])).
% 1.86/2.03 tff(9522,plain,
% 1.86/2.03 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9521])).
% 1.86/2.03 tff(9523,plain,
% 1.86/2.03 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9460])).
% 1.86/2.03 tff(9524,plain,
% 1.86/2.03 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.86/2.03 inference(symmetry,[status(thm)],[9523])).
% 1.86/2.03 tff(9525,plain,
% 1.86/2.03 (b(s(s(s(z))), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9510, 9524])).
% 1.86/2.03 tff(9526,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9527,plain,
% 1.86/2.03 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9528,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9527])).
% 1.86/2.03 tff(9529,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9528, 9526])).
% 1.86/2.03 tff(9530,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(9531,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9530, 9529])).
% 1.86/2.03 tff(9532,plain,
% 1.86/2.03 ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9531, 116])).
% 1.86/2.03 tff(9533,plain,
% 1.86/2.03 (~b(z, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9532, 9525, 9261, 9493])).
% 1.86/2.03 tff(9534,plain,
% 1.86/2.03 (~b(z, s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9533, 9522])).
% 1.86/2.03 tff(9535,plain,
% 1.86/2.03 (r(z, s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[514, 9534])).
% 1.86/2.03 tff(9536,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9537,plain,
% 1.86/2.03 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9538,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9537])).
% 1.86/2.03 tff(9539,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9538, 9536])).
% 1.86/2.03 tff(9540,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(9541,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9540, 9539])).
% 1.86/2.03 tff(9542,plain,
% 1.86/2.03 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9541, 77, 9455, 9535, 9520])).
% 1.86/2.03 tff(9543,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[898, 21, 895, 9542])).
% 1.86/2.03 tff(9544,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9545,plain,
% 1.86/2.03 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(9546,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9545])).
% 1.86/2.03 tff(9547,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9546, 9544])).
% 1.86/2.03 tff(9548,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(9549,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[9548, 9547])).
% 1.86/2.03 tff(9550,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9549, 116, 9261, 9480, 9482, 9543, 9459])).
% 1.86/2.03 tff(9551,plain,(b(s(s(s(z))), z) | b(s(s(z)), s(z)) | b(s(z), elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(9552,plain,
% 1.86/2.03 (b(s(s(s(z))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[9551, 1, 340, 4432])).
% 1.86/2.03 tff(9553,plain,
% 1.86/2.03 (~r(s(z), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[8282, 428, 3651])).
% 1.86/2.03 tff(9554,plain,
% 1.86/2.03 (s(z) = elem!1),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[357, 9553, 340])).
% 1.86/2.03 tff(9555,plain,
% 1.86/2.03 (s(s(z)) = s(elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9554])).
% 1.86/2.03 tff(9556,plain,
% 1.86/2.03 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9555])).
% 1.86/2.03 tff(9557,plain,
% 1.86/2.03 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[9556])).
% 1.86/2.03 tff(9558,plain,
% 1.86/2.03 (s(s(s(z))) = s(s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9555])).
% 1.86/2.03 tff(9559,plain,
% 1.86/2.03 (s(s(elem!1)) = s(s(s(z)))),
% 1.86/2.03 inference(symmetry,[status(thm)],[9558])).
% 1.86/2.03 tff(9560,plain,
% 1.86/2.03 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[9559])).
% 1.86/2.03 tff(9561,plain,
% 1.86/2.03 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[9560, 9557])).
% 1.86/2.03 tff(9562,plain,
% 1.86/2.03 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9561])).
% 1.86/2.04 tff(9563,plain,
% 1.86/2.04 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9555])).
% 1.86/2.04 tff(9564,plain,
% 1.86/2.04 (b(s(elem!1), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7113, 9563])).
% 1.86/2.04 tff(9565,plain,
% 1.86/2.04 (b(s(s(elem!1)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2832, 9554, 2247])).
% 1.86/2.04 tff(9566,plain,
% 1.86/2.04 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9558])).
% 1.86/2.04 tff(9567,plain,
% 1.86/2.04 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9554])).
% 1.86/2.04 tff(9568,plain,
% 1.86/2.04 (b(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[175, 9567])).
% 1.86/2.04 tff(9569,plain,
% 1.86/2.04 (b(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9568, 9566])).
% 1.86/2.04 tff(9570,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9571,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(9572,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9571, 9570])).
% 1.86/2.04 tff(9573,plain,
% 1.86/2.04 (~b(s(elem!1), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9572, 116, 1055, 9569, 9565, 9564])).
% 1.86/2.04 tff(9574,plain,
% 1.86/2.04 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9573, 9562])).
% 1.86/2.04 tff(9575,plain,
% 1.86/2.04 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9554])).
% 1.86/2.04 tff(9576,plain,
% 1.86/2.04 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9575])).
% 1.86/2.04 tff(9577,plain,
% 1.86/2.04 (~(s(s(s(z))) = elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[135, 9576])).
% 1.86/2.04 tff(9578,plain,
% 1.86/2.04 (~b(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2767, 9568, 2247, 1055])).
% 1.86/2.04 tff(9579,plain,
% 1.86/2.04 (r(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2725, 9578, 9577])).
% 1.86/2.04 tff(9580,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[4976, 9579, 428])).
% 1.86/2.04 tff(9581,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[105, 9580])).
% 1.86/2.04 tff(9582,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9581, 9574])).
% 1.86/2.04 tff(9583,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | b(s(z), elem!1) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(9584,plain,
% 1.86/2.04 (~r(s(s(z)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9583, 9125, 2247, 175, 340, 3651])).
% 1.86/2.04 tff(9585,plain,
% 1.86/2.04 (s(s(z)) = elem!1),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[426, 9584, 1])).
% 1.86/2.04 tff(9586,plain,
% 1.86/2.04 (~b(s(z), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[376, 9585, 340])).
% 1.86/2.04 tff(9587,plain,
% 1.86/2.04 (r(s(z), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[172, 9586])).
% 1.86/2.04 tff(9588,plain,
% 1.86/2.04 (~(s(z) = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[480, 9585])).
% 1.86/2.04 tff(9589,plain,
% 1.86/2.04 (r(s(z), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[357, 9588, 340])).
% 1.86/2.04 tff(9590,plain,
% 1.86/2.04 (~(s(s(elem!1)) = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[529, 9585, 8280])).
% 1.86/2.04 tff(9591,plain,
% 1.86/2.04 (b(z, s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6518, 9585, 9125])).
% 1.86/2.04 tff(9592,plain,
% 1.86/2.04 (b(elem!1, z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2403, 9585, 7113])).
% 1.86/2.04 tff(9593,plain,
% 1.86/2.04 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[836, 9585, 9590])).
% 1.86/2.04 tff(9594,plain,
% 1.86/2.04 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8306, 9593])).
% 1.86/2.04 tff(9595,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[556])).
% 1.86/2.04 tff(9596,plain,
% 1.86/2.04 (b(s(s(elem!1)), z) <=> b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(symmetry,[status(thm)],[9595])).
% 1.86/2.04 tff(9597,plain,
% 1.86/2.04 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(s(s(z)))), z))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9596])).
% 1.86/2.04 tff(9598,plain,
% 1.86/2.04 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[557])).
% 1.86/2.04 tff(9599,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(symmetry,[status(thm)],[9598])).
% 1.86/2.04 tff(9600,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[370])).
% 1.86/2.04 tff(9601,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(transitivity,[status(thm)],[9600, 9599])).
% 1.86/2.04 tff(9602,plain,
% 1.86/2.04 (~b(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5560, 7540, 2247, 1055])).
% 1.86/2.04 tff(9603,plain,
% 1.86/2.04 (r(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2725, 7622, 9602])).
% 1.86/2.04 tff(9604,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9083, 9603, 370])).
% 1.86/2.04 tff(9605,plain,
% 1.86/2.04 (b(z, s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6518, 370, 1055])).
% 1.86/2.04 tff(9606,plain,
% 1.86/2.04 (~b(elem!1, s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1063, 254, 7540, 1055])).
% 1.86/2.04 tff(9607,plain,
% 1.86/2.04 (r(elem!1, s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1068, 9606, 1362])).
% 1.86/2.04 tff(9608,plain,
% 1.86/2.04 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9607, 9121])).
% 1.86/2.04 tff(9609,plain,
% 1.86/2.04 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[336, 9608, 156])).
% 1.86/2.04 tff(9610,plain,
% 1.86/2.04 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[325, 9609])).
% 1.86/2.04 tff(9611,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2803, 9610, 7113, 2247, 9605, 156])).
% 1.86/2.04 tff(9612,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3951, 9611])).
% 1.86/2.04 tff(9613,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5905, 9612, 9604])).
% 1.86/2.04 tff(9614,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[226, 9613])).
% 1.86/2.04 tff(9615,plain,
% 1.86/2.04 (b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9614, 9601])).
% 1.86/2.04 tff(9616,plain,
% 1.86/2.04 (~b(s(s(elem!1)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7583, 116, 1055, 7540, 9615])).
% 1.86/2.04 tff(9617,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9616, 9597])).
% 1.86/2.04 tff(9618,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[254, 9617])).
% 1.86/2.04 tff(9619,plain,((~b(s(s(s(s(z)))), z)) | (~(s(s(z)) = elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(9620,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9619, 9585, 9125, 2247, 9587, 9594])).
% 1.86/2.04 tff(9621,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[247, 9620])).
% 1.86/2.04 tff(9622,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8412, 9621, 9585, 9125, 9589, 9590, 9587, 9592])).
% 1.86/2.04 tff(9623,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3951, 9622])).
% 1.86/2.04 tff(9624,plain,
% 1.86/2.04 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2803, 9623, 7113, 2247, 9591, 9587])).
% 1.86/2.04 tff(9625,plain,
% 1.86/2.04 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[325, 9624])).
% 1.86/2.04 tff(9626,plain,
% 1.86/2.04 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9585])).
% 1.86/2.04 tff(9627,plain,
% 1.86/2.04 ((~r(s(s(z)), z)) <=> (~r(elem!1, z))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9626])).
% 1.86/2.04 tff(9628,plain,
% 1.86/2.04 (~r(s(s(z)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3243, 9587, 2247, 9125, 9585, 9589, 5772])).
% 1.86/2.04 tff(9629,plain,
% 1.86/2.04 (~r(elem!1, z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9628, 9627])).
% 1.86/2.04 tff(9630,plain,
% 1.86/2.04 (~r(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8572, 9621, 9589, 1, 9594, 9629, 340, 1052])).
% 1.86/2.04 tff(9631,plain,
% 1.86/2.04 (b(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[210, 9630])).
% 1.86/2.04 tff(9632,plain,
% 1.86/2.04 (~b(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3291, 9631, 175, 2247])).
% 1.86/2.04 tff(9633,plain,
% 1.86/2.04 (r(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[289, 9632])).
% 1.86/2.04 tff(9634,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7959, 9633, 9625, 9125, 9590, 9589, 9585, 9587])).
% 1.86/2.04 tff(9635,plain,(r(z, elem!1) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(s(s(z)), elem!1) | b(s(z), elem!1) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(9636,plain,
% 1.86/2.04 (r(z, elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9635, 9552, 8278, 1, 340, 7120])).
% 1.86/2.04 tff(9637,plain,
% 1.86/2.04 (~r(s(z), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8236, 9636, 340, 1, 9552])).
% 1.86/2.04 tff(9638,plain,
% 1.86/2.04 (s(z) = elem!1),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[357, 9637, 340])).
% 1.86/2.04 tff(9639,plain,
% 1.86/2.04 (s(s(z)) = s(elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9638])).
% 1.86/2.04 tff(9640,plain,
% 1.86/2.04 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9639])).
% 1.86/2.04 tff(9641,plain,
% 1.86/2.04 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.86/2.04 inference(symmetry,[status(thm)],[9640])).
% 1.86/2.04 tff(9642,plain,
% 1.86/2.04 ((~r(z, s(elem!1))) <=> (~r(z, s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9641])).
% 1.86/2.04 tff(9643,plain,
% 1.86/2.04 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9639])).
% 1.86/2.04 tff(9644,plain,
% 1.86/2.04 (~(s(s(z)) = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[480, 9638])).
% 1.86/2.04 tff(9645,plain,
% 1.86/2.04 (r(s(s(z)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[426, 9644, 1])).
% 1.86/2.04 tff(9646,plain,
% 1.86/2.04 (r(s(elem!1), elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9645, 9643])).
% 1.86/2.04 tff(9647,plain,
% 1.86/2.04 (~r(z, s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8139, 77, 9636, 9646])).
% 1.86/2.04 tff(9648,plain,
% 1.86/2.04 (~r(z, s(s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9647, 9642])).
% 1.86/2.04 tff(9649,plain,
% 1.86/2.04 (b(z, s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1174, 9648])).
% 1.86/2.04 tff(9650,plain,
% 1.86/2.04 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8127, 9649, 7113, 9552])).
% 1.86/2.04 tff(9651,plain,
% 1.86/2.04 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[105, 9650])).
% 1.86/2.04 tff(9652,plain,
% 1.86/2.04 (s(s(s(z))) = s(s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9639])).
% 1.86/2.04 tff(9653,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9652])).
% 1.86/2.04 tff(9654,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.04 inference(symmetry,[status(thm)],[9653])).
% 1.86/2.04 tff(9655,plain,
% 1.86/2.04 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9654])).
% 1.86/2.04 tff(9656,plain,
% 1.86/2.04 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9638])).
% 1.86/2.04 tff(9657,plain,
% 1.86/2.04 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.04 inference(transitivity,[status(thm)],[9656, 4222])).
% 1.86/2.04 tff(9658,plain,
% 1.86/2.04 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9657])).
% 1.86/2.04 tff(9659,plain,
% 1.86/2.04 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[1901, 9658])).
% 1.86/2.04 tff(9660,plain,
% 1.86/2.04 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9639])).
% 1.86/2.04 tff(9661,plain,
% 1.86/2.04 (b(s(elem!1), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7113, 9660])).
% 1.86/2.04 tff(9662,plain,
% 1.86/2.04 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1531, 9638])).
% 1.86/2.04 tff(9663,plain,
% 1.86/2.04 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1364, 9662])).
% 1.86/2.04 tff(9664,plain,
% 1.86/2.04 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9639])).
% 1.86/2.04 tff(9665,plain,
% 1.86/2.04 (b(z, s(elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9649, 9664])).
% 1.86/2.04 tff(9666,plain,
% 1.86/2.04 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9059, 9665, 9636, 9663, 9646, 9661])).
% 1.86/2.04 tff(9667,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[885, 9666, 9659])).
% 1.86/2.04 tff(9668,plain,
% 1.86/2.04 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9652])).
% 1.86/2.04 tff(9669,plain,
% 1.86/2.04 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9638])).
% 1.86/2.04 tff(9670,plain,
% 1.86/2.04 (b(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[8278, 9669])).
% 1.86/2.04 tff(9671,plain,
% 1.86/2.04 (b(elem!1, s(s(elem!1)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9670, 9668])).
% 1.86/2.04 tff(9672,plain,
% 1.86/2.04 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9638])).
% 1.86/2.04 tff(9673,plain,
% 1.86/2.04 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9672])).
% 1.86/2.04 tff(9674,plain,
% 1.86/2.04 (~(s(s(elem!1)) = elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[566, 9673])).
% 1.86/2.04 tff(9675,plain,
% 1.86/2.04 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9639])).
% 1.86/2.04 tff(9676,plain,
% 1.86/2.04 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.86/2.04 inference(transitivity,[status(thm)],[9675, 1820])).
% 1.86/2.04 tff(9677,plain,
% 1.86/2.04 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9676])).
% 1.86/2.04 tff(9678,plain,
% 1.86/2.04 (~(s(s(elem!1)) = s(elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9489, 9677])).
% 1.86/2.04 tff(9679,plain,
% 1.86/2.04 (b(s(s(elem!1)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2832, 9638, 9552])).
% 1.86/2.04 tff(9680,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9681,plain,
% 1.86/2.04 (((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9682,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9681])).
% 1.86/2.04 tff(9683,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[9682, 9680])).
% 1.86/2.04 tff(9684,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(9685,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9684, 9683])).
% 1.86/2.04 tff(9686,plain,
% 1.86/2.04 (~b(s(s(elem!1)), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9685, 116, 9679, 9661, 9665])).
% 1.86/2.04 tff(9687,plain,
% 1.86/2.04 (r(s(s(elem!1)), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[767, 9686, 9678])).
% 1.86/2.04 tff(9688,plain,
% 1.86/2.04 (~r(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2865, 9687, 9638, 9645])).
% 1.86/2.04 tff(9689,plain,
% 1.86/2.04 (b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[743, 9688, 9674])).
% 1.86/2.04 tff(9690,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9691,plain,
% 1.86/2.04 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9692,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9691])).
% 1.86/2.04 tff(9693,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[9692, 9690])).
% 1.86/2.04 tff(9694,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(9695,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9694, 9693])).
% 1.86/2.04 tff(9696,plain,
% 1.86/2.04 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9695, 116, 9689, 9671, 9667])).
% 1.86/2.04 tff(9697,plain,
% 1.86/2.04 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9696, 9655])).
% 1.86/2.04 tff(9698,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5016, 9697, 9651])).
% 1.86/2.04 tff(9699,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3951, 9698])).
% 1.86/2.04 tff(9700,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2016, 9699, 9638])).
% 1.86/2.04 tff(9701,plain,
% 1.86/2.04 (~b(elem!1, s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3448, 116, 9689, 9671, 9700])).
% 1.86/2.04 tff(9702,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1542, 9701, 9638, 9645])).
% 1.86/2.04 tff(9703,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[149, 9702])).
% 1.86/2.04 tff(9704,plain,
% 1.86/2.04 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1584, 9662])).
% 1.86/2.04 tff(9705,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3455, 116, 9689, 9671, 9700])).
% 1.86/2.04 tff(9706,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1596, 9705, 9704])).
% 1.86/2.04 tff(9707,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3287, 9706, 9636])).
% 1.86/2.04 tff(9708,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[247, 9707])).
% 1.86/2.04 tff(9709,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2450, 9708, 9703, 9552, 9649, 9699])).
% 1.86/2.04 tff(9710,plain,(b(s(s(z)), elem!1) | b(s(z), elem!1) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(9711,plain,
% 1.86/2.04 (b(s(s(z)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9710, 340, 4432])).
% 1.86/2.04 tff(9712,plain,
% 1.86/2.04 (~(s(z) = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[4434, 9711, 4432])).
% 1.86/2.04 tff(9713,plain,
% 1.86/2.04 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1709])).
% 1.86/2.04 tff(9714,plain,
% 1.86/2.04 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(symmetry,[status(thm)],[9713])).
% 1.86/2.04 tff(9715,plain,
% 1.86/2.04 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1784, 1709])).
% 1.86/2.04 tff(9716,plain,
% 1.86/2.04 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(transitivity,[status(thm)],[9715, 9714])).
% 1.86/2.04 tff(9717,plain,
% 1.86/2.04 (r(s(s(elem!1)), s(z))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3651, 9716])).
% 1.86/2.04 tff(9718,plain,
% 1.86/2.04 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.86/2.04 inference(symmetry,[status(thm)],[4809])).
% 1.86/2.04 tff(9719,plain,
% 1.86/2.04 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(z), s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9718])).
% 1.86/2.04 tff(9720,plain,
% 1.86/2.04 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1709])).
% 1.86/2.04 tff(9721,plain,
% 1.86/2.04 (b(s(elem!1), s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[175, 9720])).
% 1.86/2.04 tff(9722,plain,
% 1.86/2.04 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[442])).
% 1.86/2.04 tff(9723,plain,
% 1.86/2.04 (r(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[64, 9722])).
% 1.86/2.04 tff(9724,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9725,plain,
% 1.86/2.04 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9726,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9725])).
% 1.86/2.04 tff(9727,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[9726, 9724])).
% 1.86/2.04 tff(9728,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(9729,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9728, 9727])).
% 1.86/2.04 tff(9730,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9729, 77, 9723, 650])).
% 1.86/2.04 tff(9731,plain,
% 1.86/2.04 (b(s(s(s(z))), s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1853, 9730, 1783])).
% 1.86/2.04 tff(9732,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3961, 228, 64])).
% 1.86/2.04 tff(9733,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3951, 9732])).
% 1.86/2.04 tff(9734,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9448, 9733, 340, 1052, 57])).
% 1.86/2.04 tff(9735,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[105, 9734])).
% 1.86/2.04 tff(9736,plain,
% 1.86/2.04 (b(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9735, 8075])).
% 1.86/2.04 tff(9737,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[8492, 228, 4842, 64])).
% 1.86/2.04 tff(9738,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[226, 9737])).
% 1.86/2.04 tff(9739,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3559, 9738, 1713])).
% 1.86/2.04 tff(9740,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9741,plain,
% 1.86/2.04 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9742,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[9741])).
% 1.86/2.04 tff(9743,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[9742, 9740])).
% 1.86/2.04 tff(9744,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(9745,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[9744, 9743])).
% 1.86/2.04 tff(9746,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9745, 116, 9733, 9739, 6286, 9736, 6842])).
% 1.86/2.04 tff(9747,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~(z = elem!1)) | b(s(z), elem!1) | r(z, elem!1) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(9748,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[9747, 9731, 9721, 442, 340, 1052, 57])).
% 1.86/2.04 tff(9749,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[247, 9748])).
% 1.86/2.04 tff(9750,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2421, 9748, 1713])).
% 1.86/2.04 tff(9751,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1596, 9750, 3578])).
% 1.86/2.04 tff(9752,plain,
% 1.86/2.04 (~b(z, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3377, 2023, 8085, 254])).
% 1.86/2.04 tff(9753,plain,
% 1.86/2.04 (r(z, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[514, 9752])).
% 1.86/2.04 tff(9754,plain,
% 1.86/2.04 (~r(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3185, 9753, 794])).
% 1.86/2.04 tff(9755,plain,
% 1.86/2.04 (b(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[289, 9754])).
% 1.86/2.04 tff(9756,plain,
% 1.86/2.04 (b(elem!1, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6231, 9755, 442])).
% 1.86/2.04 tff(9757,plain,
% 1.86/2.04 (b(elem!1, s(elem!1))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6238, 9756, 442])).
% 1.86/2.04 tff(9758,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9759,plain,
% 1.86/2.04 (((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(9760,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9759])).
% 1.86/2.05 tff(9761,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9760, 9758])).
% 1.86/2.05 tff(9762,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9763,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9762, 9761])).
% 1.86/2.05 tff(9764,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9763, 116, 8086, 2023, 9757, 1725, 6842])).
% 1.86/2.05 tff(9765,plain,((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(9766,plain,
% 1.86/2.05 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9765, 9751, 9721, 442, 794, 9749])).
% 1.86/2.05 tff(9767,plain,
% 1.86/2.05 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3559, 9766, 1713])).
% 1.86/2.05 tff(9768,plain,
% 1.86/2.05 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[226, 9767])).
% 1.86/2.05 tff(9769,plain,
% 1.86/2.05 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9768, 1855])).
% 1.86/2.05 tff(9770,plain,
% 1.86/2.05 ((s(elem!1) = s(s(s(s(z))))) <=> (s(z) = s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[1710])).
% 1.86/2.05 tff(9771,plain,
% 1.86/2.05 ((s(z) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[9770])).
% 1.86/2.05 tff(9772,plain,
% 1.86/2.05 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9771])).
% 1.86/2.05 tff(9773,plain,
% 1.86/2.05 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[320, 9772])).
% 1.86/2.05 tff(9774,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9775,plain,
% 1.86/2.05 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9776,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9775])).
% 1.86/2.05 tff(9777,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9776, 9774])).
% 1.86/2.05 tff(9778,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9779,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9778, 9777])).
% 1.86/2.05 tff(9780,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9779, 77, 3953, 2608, 5696])).
% 1.86/2.05 tff(9781,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(9782,plain,
% 1.86/2.05 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9781, 3953, 5696])).
% 1.86/2.05 tff(9783,plain,
% 1.86/2.05 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2605, 9782, 442])).
% 1.86/2.05 tff(9784,plain,
% 1.86/2.05 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[105, 9783])).
% 1.86/2.05 tff(9785,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9784, 8075])).
% 1.86/2.05 tff(9786,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9787,plain,
% 1.86/2.05 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9788,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9787])).
% 1.86/2.05 tff(9789,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9788, 9786])).
% 1.86/2.05 tff(9790,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9791,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9790, 9789])).
% 1.86/2.05 tff(9792,plain,
% 1.86/2.05 (~b(s(elem!1), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9791, 116, 6286, 9785, 9721])).
% 1.86/2.05 tff(9793,plain,
% 1.86/2.05 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1836, 21, 9792])).
% 1.86/2.05 tff(9794,plain,
% 1.86/2.05 (r(s(elem!1), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9793, 1823])).
% 1.86/2.05 tff(9795,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9796,plain,
% 1.86/2.05 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9797,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9796])).
% 1.86/2.05 tff(9798,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9797, 9795])).
% 1.86/2.05 tff(9799,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9800,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9799, 9798])).
% 1.86/2.05 tff(9801,plain,
% 1.86/2.05 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9800, 77, 3953, 5696, 9794])).
% 1.86/2.05 tff(9802,plain,
% 1.86/2.05 (((~![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))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9803,plain,
% 1.86/2.05 ((~![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))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9804,plain,
% 1.86/2.05 ((~![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)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9803, 9802])).
% 1.86/2.05 tff(9805,plain,
% 1.86/2.05 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9804, 21, 9801])).
% 1.86/2.05 tff(9806,plain,
% 1.86/2.05 (b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9805, 9773])).
% 1.86/2.05 tff(9807,plain,
% 1.86/2.05 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[8996, 77, 5696, 9794])).
% 1.86/2.05 tff(9808,plain,
% 1.86/2.05 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1776, 21, 9807])).
% 1.86/2.05 tff(9809,plain,
% 1.86/2.05 (b(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9808, 1757])).
% 1.86/2.05 tff(9810,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9811,plain,
% 1.86/2.05 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(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(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9812,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9811])).
% 1.86/2.05 tff(9813,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9812, 9810])).
% 1.86/2.05 tff(9814,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9815,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9814, 9813])).
% 1.86/2.05 tff(9816,plain,
% 1.86/2.05 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9815, 116, 9809, 9806, 6286])).
% 1.86/2.05 tff(9817,plain,
% 1.86/2.05 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1146, 9816])).
% 1.86/2.05 tff(9818,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[1785])).
% 1.86/2.05 tff(9819,plain,
% 1.86/2.05 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[1784])).
% 1.86/2.05 tff(9820,plain,
% 1.86/2.05 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9819, 7690])).
% 1.86/2.05 tff(9821,plain,
% 1.86/2.05 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9820])).
% 1.86/2.05 tff(9822,plain,
% 1.86/2.05 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[100, 9821])).
% 1.86/2.05 tff(9823,plain,
% 1.86/2.05 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[1784])).
% 1.86/2.05 tff(9824,plain,
% 1.86/2.05 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[1784])).
% 1.86/2.05 tff(9825,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[9824])).
% 1.86/2.05 tff(9826,plain,
% 1.86/2.05 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9825])).
% 1.86/2.05 tff(9827,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9828,plain,
% 1.86/2.05 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9829,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9828])).
% 1.86/2.05 tff(9830,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9829, 9827])).
% 1.86/2.05 tff(9831,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9832,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9831, 9830])).
% 1.86/2.05 tff(9833,plain,
% 1.86/2.05 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9832, 116, 8086, 1879, 1725])).
% 1.86/2.05 tff(9834,plain,
% 1.86/2.05 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9833, 9826])).
% 1.86/2.05 tff(9835,plain,
% 1.86/2.05 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[149, 9834])).
% 1.86/2.05 tff(9836,plain,
% 1.86/2.05 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9835, 9823])).
% 1.86/2.05 tff(9837,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9838,plain,
% 1.86/2.05 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9839,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[9838])).
% 1.86/2.05 tff(9840,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[9839, 9837])).
% 1.86/2.05 tff(9841,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(9842,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9841, 9840])).
% 1.86/2.05 tff(9843,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[9842, 77, 2453, 9836])).
% 1.86/2.05 tff(9844,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[664, 9843, 9822])).
% 1.86/2.05 tff(9845,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[9844, 9818])).
% 1.86/2.05 tff(9846,plain,
% 1.86/2.05 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6403, 9845, 175, 27])).
% 1.86/2.05 tff(9847,plain,
% 1.86/2.05 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1380, 9846])).
% 1.86/2.05 tff(9848,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(9849,plain,
% 1.86/2.05 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9850,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9849])).
% 1.86/2.06 tff(9851,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[9850, 9848])).
% 1.86/2.06 tff(9852,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(9853,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9852, 9851])).
% 1.86/2.06 tff(9854,plain,
% 1.86/2.06 (~b(elem!1, s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9853, 116, 8086, 1879, 9844])).
% 1.86/2.06 tff(9855,plain,
% 1.86/2.06 (r(elem!1, s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1345, 9854, 1620])).
% 1.86/2.06 tff(9856,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9857,plain,
% 1.86/2.06 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9858,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9857])).
% 1.86/2.06 tff(9859,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[9858, 9856])).
% 1.86/2.06 tff(9860,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(9861,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9860, 9859])).
% 1.86/2.06 tff(9862,plain,
% 1.86/2.06 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9861, 77, 9855, 9847])).
% 1.86/2.06 tff(9863,plain,
% 1.86/2.06 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[885, 9862, 1896])).
% 1.86/2.06 tff(9864,plain,
% 1.86/2.06 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[4709, 77, 3953, 9847])).
% 1.86/2.06 tff(9865,plain,
% 1.86/2.06 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6694, 9864])).
% 1.86/2.06 tff(9866,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9867,plain,
% 1.86/2.06 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9868,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9867])).
% 1.86/2.06 tff(9869,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[9868, 9866])).
% 1.86/2.06 tff(9870,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(9871,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9870, 9869])).
% 1.86/2.06 tff(9872,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9871, 116, 8086, 1879, 9865, 1725, 9863])).
% 1.86/2.06 tff(9873,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(9874,plain,
% 1.86/2.06 (~b(elem!1, s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9873, 3953, 1725, 1620, 175, 9784, 442, 9817])).
% 1.86/2.06 tff(9875,plain,
% 1.86/2.06 (r(elem!1, s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1892, 9874, 1876])).
% 1.86/2.06 tff(9876,plain,
% 1.86/2.06 (~r(elem!1, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[802, 9875, 794])).
% 1.86/2.06 tff(9877,plain,
% 1.86/2.06 (b(elem!1, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[633, 9876, 1046])).
% 1.86/2.06 tff(9878,plain,
% 1.86/2.06 (b(elem!1, s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6238, 9877, 442])).
% 1.86/2.06 tff(9879,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9880,plain,
% 1.86/2.06 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9881,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9880])).
% 1.86/2.06 tff(9882,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[9881, 9879])).
% 1.86/2.06 tff(9883,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(9884,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9883, 9882])).
% 1.86/2.06 tff(9885,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9884, 116, 9809, 9806, 9878, 1725])).
% 1.86/2.06 tff(9886,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (elem!1 = s(z)) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(9887,plain,
% 1.86/2.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9886, 9751, 442, 1046, 794, 5772, 175, 9731, 9769])).
% 1.86/2.06 tff(9888,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3951, 9887])).
% 1.86/2.06 tff(9889,plain,
% 1.86/2.06 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9448, 9888, 340, 1052, 57])).
% 1.86/2.06 tff(9890,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[105, 9889])).
% 1.86/2.06 tff(9891,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9890, 8075])).
% 1.86/2.06 tff(9892,plain,
% 1.86/2.06 (~b(s(elem!1), s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9791, 116, 9731, 9891, 9721])).
% 1.86/2.06 tff(9893,plain,
% 1.86/2.06 (~b(s(z), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9892, 9719])).
% 1.86/2.06 tff(9894,plain,
% 1.86/2.06 (r(s(z), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[172, 9893])).
% 1.86/2.06 tff(9895,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9896,plain,
% 1.86/2.06 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9897,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9896])).
% 1.86/2.06 tff(9898,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[9897, 9895])).
% 1.86/2.06 tff(9899,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(9900,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9899, 9898])).
% 1.86/2.06 tff(9901,plain,
% 1.86/2.06 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9900, 116, 9888, 9731, 9891, 9721])).
% 1.86/2.06 tff(9902,plain,
% 1.86/2.06 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9901, 9826])).
% 1.86/2.06 tff(9903,plain,
% 1.86/2.06 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[149, 9902])).
% 1.86/2.06 tff(9904,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9905,plain,
% 1.86/2.06 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9906,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9905])).
% 1.86/2.06 tff(9907,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[9906, 9904])).
% 1.86/2.06 tff(9908,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(9909,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9908, 9907])).
% 1.86/2.06 tff(9910,plain,
% 1.86/2.06 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9909, 116, 9888, 9731, 9721])).
% 1.86/2.06 tff(9911,plain,
% 1.86/2.06 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9910, 1800])).
% 1.86/2.06 tff(9912,plain,
% 1.86/2.06 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[325, 9911])).
% 1.86/2.06 tff(9913,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[336, 9912, 9903, 9894])).
% 1.86/2.06 tff(9914,plain,(b(s(s(s(z))), z) | (~(z = elem!1)) | b(s(z), elem!1) | r(z, elem!1) | (elem!1 = s(z)) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(9915,plain,
% 1.86/2.06 (b(s(s(s(z))), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9914, 442, 340, 1052, 1046, 9717, 175, 4806])).
% 1.86/2.06 tff(9916,plain,
% 1.86/2.06 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[1710])).
% 1.86/2.06 tff(9917,plain,
% 1.86/2.06 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[9916])).
% 1.86/2.06 tff(9918,plain,
% 1.86/2.06 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[442])).
% 1.86/2.06 tff(9919,plain,
% 1.86/2.06 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[442])).
% 1.86/2.06 tff(9920,plain,
% 1.86/2.06 ((~r(s(s(z)), z)) <=> (~r(s(s(z)), elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9919])).
% 1.86/2.06 tff(9921,plain,
% 1.86/2.06 (~r(s(s(z)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2393, 2247, 28, 2235])).
% 1.86/2.06 tff(9922,plain,
% 1.86/2.06 (~r(s(s(z)), elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9921, 9920])).
% 1.86/2.06 tff(9923,plain,
% 1.86/2.06 (~r(s(z), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3274, 3545, 340, 28, 2247, 9922])).
% 1.86/2.06 tff(9924,plain,
% 1.86/2.06 (b(s(z), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[172, 9923])).
% 1.86/2.06 tff(9925,plain,
% 1.86/2.06 (~(elem!1 = s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2407, 3545, 2247])).
% 1.86/2.06 tff(9926,plain,
% 1.86/2.06 (b(s(s(s(z))), elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2247, 3547])).
% 1.86/2.06 tff(9927,plain,
% 1.86/2.06 (~r(s(z), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7144, 271, 1303, 2235])).
% 1.86/2.06 tff(9928,plain,
% 1.86/2.06 (b(s(z), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[194, 9927])).
% 1.86/2.06 tff(9929,plain,
% 1.86/2.06 (b(s(elem!1), s(s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[9928, 9720])).
% 1.86/2.06 tff(9930,plain,
% 1.86/2.06 (b(elem!1, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6231, 271, 442])).
% 1.86/2.06 tff(9931,plain,
% 1.86/2.06 (b(elem!1, s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6238, 9930, 442])).
% 1.86/2.06 tff(9932,plain,
% 1.86/2.06 (~b(z, s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9348, 271, 1303, 174])).
% 1.86/2.06 tff(9933,plain,
% 1.86/2.06 (r(z, s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1174, 9932])).
% 1.86/2.06 tff(9934,plain,
% 1.86/2.06 (~r(z, s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[9352, 9933, 2235])).
% 1.86/2.06 tff(9935,plain,
% 1.86/2.06 (~r(elem!1, s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2488, 9934, 1713])).
% 1.86/2.06 tff(9936,plain,
% 1.86/2.06 (b(elem!1, s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1345, 9935, 1620])).
% 1.86/2.06 tff(9937,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9938,plain,
% 1.86/2.06 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(9939,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[9938])).
% 1.86/2.06 tff(9940,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[9939, 9937])).
% 1.86/2.07 tff(9941,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(9942,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9941, 9940])).
% 1.86/2.07 tff(9943,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9942, 116, 3561, 9936, 9931, 9929])).
% 1.86/2.07 tff(9944,plain,((~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(9945,plain,
% 1.86/2.07 (~b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9944, 9926, 442, 9925, 2235, 9153, 9924])).
% 1.86/2.07 tff(9946,plain,
% 1.86/2.07 (r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[289, 9945])).
% 1.86/2.07 tff(9947,plain,
% 1.86/2.07 (r(elem!1, s(z))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9946, 9918])).
% 1.86/2.07 tff(9948,plain,
% 1.86/2.07 (r(elem!1, s(elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9947, 9917])).
% 1.86/2.07 tff(9949,plain,
% 1.86/2.07 (r(s(z), elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[4842, 5028])).
% 1.86/2.07 tff(9950,plain,
% 1.86/2.07 (r(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2605, 442, 2235])).
% 1.86/2.07 tff(9951,plain,
% 1.86/2.07 (b(s(s(elem!1)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7170, 1713, 9153])).
% 1.86/2.07 tff(9952,plain,
% 1.86/2.07 (b(s(s(elem!1)), elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9951, 8084])).
% 1.86/2.07 tff(9953,plain,
% 1.86/2.07 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[1902, 4213])).
% 1.86/2.07 tff(9954,plain,
% 1.86/2.07 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[1709])).
% 1.86/2.07 tff(9955,plain,
% 1.86/2.07 (r(s(elem!1), s(s(s(z))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[292, 9954])).
% 1.86/2.07 tff(9956,plain,
% 1.86/2.07 (~r(elem!1, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[368, 292, 360])).
% 1.86/2.07 tff(9957,plain,
% 1.86/2.07 (b(elem!1, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1345, 9956, 9925])).
% 1.86/2.07 tff(9958,plain,
% 1.86/2.07 (b(z, s(s(s(z))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9957, 3532])).
% 1.86/2.07 tff(9959,plain,
% 1.86/2.07 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[8555, 6647])).
% 1.86/2.07 tff(9960,plain,
% 1.86/2.07 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9959, 9958, 28, 2247, 293])).
% 1.86/2.07 tff(9961,plain,
% 1.86/2.07 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1380, 9960])).
% 1.86/2.07 tff(9962,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9963,plain,
% 1.86/2.07 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9964,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[9963])).
% 1.86/2.07 tff(9965,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[9964, 9962])).
% 1.86/2.07 tff(9966,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(9967,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9966, 9965])).
% 1.86/2.07 tff(9968,plain,
% 1.86/2.07 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9967, 77, 9961, 4806, 9955])).
% 1.86/2.07 tff(9969,plain,
% 1.86/2.07 ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4324, 21, 9968])).
% 1.86/2.07 tff(9970,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9969, 9953])).
% 1.86/2.07 tff(9971,plain,
% 1.86/2.07 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[1955, 4824])).
% 1.86/2.07 tff(9972,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9973,plain,
% 1.86/2.07 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9974,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[9973])).
% 1.86/2.07 tff(9975,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[9974, 9972])).
% 1.86/2.07 tff(9976,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(9977,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9976, 9975])).
% 1.86/2.07 tff(9978,plain,
% 1.86/2.07 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9977, 77, 2608, 9961])).
% 1.86/2.07 tff(9979,plain,
% 1.86/2.07 ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4828, 21, 9978])).
% 1.86/2.07 tff(9980,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9979, 9971])).
% 1.86/2.07 tff(9981,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9982,plain,
% 1.86/2.07 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9983,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[9982])).
% 1.86/2.07 tff(9984,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[9983, 9981])).
% 1.86/2.07 tff(9985,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(9986,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9985, 9984])).
% 1.86/2.07 tff(9987,plain,
% 1.86/2.07 (~r(s(elem!1), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9986, 77, 2608, 9955])).
% 1.86/2.07 tff(9988,plain,
% 1.86/2.07 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1836, 21, 9987])).
% 1.86/2.07 tff(9989,plain,
% 1.86/2.07 (b(s(elem!1), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9988, 1823])).
% 1.86/2.07 tff(9990,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9991,plain,
% 1.86/2.07 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(9992,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[9991])).
% 1.86/2.07 tff(9993,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[9992, 9990])).
% 1.86/2.07 tff(9994,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(9995,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9994, 9993])).
% 1.86/2.07 tff(9996,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9995, 116, 616, 9957, 9989, 9980, 9970])).
% 1.86/2.07 tff(9997,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~(z = elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(9998,plain,
% 1.86/2.07 (~r(s(z), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9997, 9952, 9950, 28, 2247, 9946, 442, 9949])).
% 1.86/2.07 tff(9999,plain,
% 1.86/2.07 (b(s(z), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[194, 9998])).
% 1.86/2.07 tff(10000,plain,
% 1.86/2.07 (b(s(elem!1), s(s(s(z))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[9999, 9720])).
% 1.86/2.07 tff(10001,plain,
% 1.86/2.07 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[1784])).
% 1.86/2.07 tff(10002,plain,
% 1.86/2.07 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[442])).
% 1.86/2.07 tff(10003,plain,
% 1.86/2.07 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[10002, 10001])).
% 1.86/2.07 tff(10004,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(10005,plain,
% 1.86/2.07 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(10006,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[10005])).
% 1.86/2.07 tff(10007,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[10006, 10004])).
% 1.86/2.07 tff(10008,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(10009,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[10008, 10007])).
% 1.86/2.07 tff(10010,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[10009, 116, 3561, 1332, 28, 7391, 6842])).
% 1.86/2.07 tff(10011,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(10012,plain,
% 1.86/2.07 (~b(elem!1, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[10011, 7391, 28, 3561, 6842])).
% 1.86/2.07 tff(10013,plain,
% 1.86/2.07 (r(elem!1, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1345, 10012, 1620])).
% 1.86/2.07 tff(10014,plain,
% 1.86/2.07 (r(z, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2488, 10013, 1713])).
% 1.86/2.07 tff(10015,plain,
% 1.86/2.07 (~r(z, s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[9352, 10014, 2235])).
% 1.86/2.07 tff(10016,plain,
% 1.86/2.07 (b(z, s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1174, 10015])).
% 1.86/2.07 tff(10017,plain,
% 1.86/2.07 (b(elem!1, s(s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[10016, 10003])).
% 1.86/2.07 tff(10018,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(10019,plain,
% 1.86/2.07 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(10020,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[10019])).
% 1.86/2.07 tff(10021,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[10020, 10018])).
% 1.86/2.07 tff(10022,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(10023,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[10022, 10021])).
% 1.86/2.07 tff(10024,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[10023, 116, 10017, 3561, 28, 7391, 6842])).
% 1.86/2.07 tff(10025,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~(z = elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(10026,plain,
% 1.86/2.07 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[10025, 9926, 28, 10000, 442, 2235, 9925])).
% 1.86/2.07 tff(10027,plain,
% 1.86/2.07 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[10026, 1800])).
% 1.86/2.07 tff(10028,plain,
% 1.86/2.07 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[325, 10027])).
% 1.86/2.07 tff(10029,plain,
% 1.86/2.07 (r(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[10028, 1797])).
% 1.86/2.07 tff(10030,plain,
% 1.86/2.07 (~r(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[8864, 10028, 4842])).
% 1.86/2.07 tff(10031,plain,
% 1.86/2.07 (b(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[247, 10030])).
% 1.86/2.07 tff(10032,plain,
% 1.86/2.07 (~b(z, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3100, 10031, 28, 2247])).
% 1.86/2.07 tff(10033,plain,
% 1.86/2.07 (~b(elem!1, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3626, 10032, 442])).
% 1.86/2.07 tff(10034,plain,
% 1.86/2.07 (r(elem!1, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1068, 10033, 1718])).
% 1.86/2.07 tff(10035,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(10036,plain,
% 1.86/2.07 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(10037,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[10036])).
% 1.86/2.07 tff(10038,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[10037, 10035])).
% 1.86/2.07 tff(10039,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(10040,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[10039, 10038])).
% 1.86/2.07 tff(10041,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[10040, 77, 10034, 10029, 9948])).
% 1.86/2.07 tff(10042,plain,((~(z = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(10043,plain,
% 1.86/2.07 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[10042, 28, 442, 2247, 340])).
% 1.86/2.07 tff(10044,plain,
% 1.86/2.07 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[105, 10043])).
% 1.86/2.07 tff(10045,plain,
% 1.86/2.07 (~b(z, s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[8127, 10044, 7113, 2247])).
% 1.86/2.07 tff(10046,plain,
% 1.86/2.07 (r(z, s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1174, 10045])).
% 1.86/2.07 tff(10047,plain,
% 1.86/2.07 (~r(s(z), s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2894, 28, 7113, 1331, 2247, 340, 1052, 1718, 422, 1455])).
% 1.86/2.07 tff(10048,plain,
% 1.86/2.07 (b(s(z), s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[172, 10047])).
% 1.86/2.07 tff(10049,plain,
% 1.86/2.07 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[442])).
% 1.86/2.07 tff(10050,plain,
% 1.86/2.07 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.86/2.07 inference(symmetry,[status(thm)],[10049])).
% 1.86/2.07 tff(10051,plain,
% 1.86/2.07 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[1784])).
% 1.86/2.07 tff(10052,plain,
% 1.86/2.07 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[442])).
% 1.86/2.07 tff(10053,plain,
% 1.86/2.07 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[10052, 10051, 10050])).
% 1.86/2.07 tff(10054,plain,
% 1.86/2.07 (r(z, s(s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[10046, 10053])).
% 1.86/2.07 tff(10055,plain,
% 1.86/2.07 (~r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3185, 10054, 794])).
% 1.86/2.07 tff(10056,plain,
% 1.86/2.07 (b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[289, 10055])).
% 1.86/2.07 tff(10057,plain,
% 1.86/2.07 (~b(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3422, 10056, 2247, 28, 10048])).
% 1.86/2.07 tff(10058,plain,
% 1.86/2.07 (r(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[247, 10057])).
% 1.86/2.07 tff(10059,plain,
% 1.86/2.07 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3723, 10056, 2247, 28, 10044])).
% 1.86/2.07 tff(10060,plain,
% 1.86/2.07 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[226, 10059])).
% 1.86/2.08 tff(10061,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2549, 10060, 10058, 10046])).
% 1.86/2.08 tff(10062,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(z))) | (~(z = elem!1)) | b(s(z), elem!1) | (~b(s(s(z)), elem!1)) | r(z, elem!1) | (s(s(z)) = elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(10063,plain,
% 1.86/2.08 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10062, 9915, 9717, 442, 340, 1331, 1052, 422, 1455])).
% 1.86/2.08 tff(10064,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3951, 10063])).
% 1.86/2.08 tff(10065,plain,
% 1.86/2.08 (b(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[9915, 3547])).
% 1.86/2.08 tff(10066,plain,
% 1.86/2.08 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7350, 77, 3584, 650])).
% 1.86/2.08 tff(10067,plain,
% 1.86/2.08 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1776, 21, 10066])).
% 1.86/2.08 tff(10068,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10067, 1757])).
% 1.86/2.08 tff(10069,plain,
% 1.86/2.08 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7376, 77, 3584, 650])).
% 1.86/2.08 tff(10070,plain,
% 1.86/2.08 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[9804, 21, 10069])).
% 1.86/2.08 tff(10071,plain,
% 1.86/2.08 (b(s(elem!1), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10070, 9773])).
% 1.86/2.08 tff(10072,plain,
% 1.86/2.08 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[8075])).
% 1.86/2.08 tff(10073,plain,
% 1.86/2.08 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10072])).
% 1.86/2.08 tff(10074,plain,
% 1.86/2.08 (~r(z, s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5649, 3552, 3953])).
% 1.86/2.08 tff(10075,plain,
% 1.86/2.08 (~r(elem!1, s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2488, 10074, 1713])).
% 1.86/2.08 tff(10076,plain,
% 1.86/2.08 (b(elem!1, s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1345, 10075, 1620])).
% 1.86/2.08 tff(10077,plain,
% 1.86/2.08 (((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10078,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10077])).
% 1.86/2.08 tff(10079,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[10078, 8087])).
% 1.86/2.08 tff(10080,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(10081,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10080, 10079])).
% 1.86/2.08 tff(10082,plain,
% 1.86/2.08 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10081, 116, 8086, 3561, 10076])).
% 1.86/2.08 tff(10083,plain,
% 1.86/2.08 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10082, 10073])).
% 1.86/2.08 tff(10084,plain,
% 1.86/2.08 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[105, 10083])).
% 1.86/2.08 tff(10085,plain,
% 1.86/2.08 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5016, 10084, 3953])).
% 1.86/2.08 tff(10086,plain,
% 1.86/2.08 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10087,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10086])).
% 1.86/2.08 tff(10088,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[10087, 9937])).
% 1.86/2.08 tff(10089,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(10090,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10089, 10088])).
% 1.86/2.08 tff(10091,plain,
% 1.86/2.08 (~b(elem!1, s(elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10090, 116, 3561, 10076, 6842])).
% 1.86/2.08 tff(10092,plain,
% 1.86/2.08 (~b(elem!1, s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6238, 10091, 442])).
% 1.86/2.08 tff(10093,plain,
% 1.86/2.08 (r(elem!1, s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[633, 10092, 1046])).
% 1.86/2.08 tff(10094,plain,
% 1.86/2.08 (~r(elem!1, s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[802, 10093, 794])).
% 1.86/2.08 tff(10095,plain,
% 1.86/2.08 (b(elem!1, s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1892, 10094, 1876])).
% 1.86/2.08 tff(10096,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~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))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10097,plain,
% 1.86/2.08 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~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))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10098,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~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)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10097])).
% 1.86/2.08 tff(10099,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~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))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[10098, 10096])).
% 1.86/2.08 tff(10100,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(10101,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10100, 10099])).
% 1.86/2.08 tff(10102,plain,
% 1.86/2.08 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10101, 116, 10095, 3561, 10076, 10085])).
% 1.86/2.08 tff(10103,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[885, 10102, 1896])).
% 1.86/2.08 tff(10104,plain,
% 1.86/2.08 ((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7399, 6647])).
% 1.86/2.08 tff(10105,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10104, 10103, 10071, 3552, 1902, 3584, 10068, 650])).
% 1.86/2.08 tff(10106,plain,(b(s(s(s(s(z)))), z) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(z)) | (~b(s(elem!1), s(s(s(z))))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(10107,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10106, 4806, 10065, 442, 10064, 9717, 1046, 9721, 5772])).
% 1.86/2.08 tff(10108,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10107, 1719])).
% 1.86/2.08 tff(10109,plain,
% 1.86/2.08 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[9765, 10108, 9721, 442, 9717, 10107])).
% 1.86/2.08 tff(10110,plain,
% 1.86/2.08 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3559, 10109, 1713])).
% 1.86/2.08 tff(10111,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[226, 10110])).
% 1.86/2.08 tff(10112,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10111, 1855])).
% 1.86/2.08 tff(10113,plain,
% 1.86/2.08 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[9781, 10112, 10064])).
% 1.86/2.08 tff(10114,plain,
% 1.86/2.08 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2605, 10113, 442])).
% 1.86/2.08 tff(10115,plain,
% 1.86/2.08 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[105, 10114])).
% 1.86/2.08 tff(10116,plain,
% 1.86/2.08 (b(s(s(elem!1)), s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10115, 8075])).
% 1.86/2.08 tff(10117,plain,
% 1.86/2.08 (~b(z, s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8127, 10115, 7113, 9915])).
% 1.86/2.08 tff(10118,plain,
% 1.86/2.08 (r(z, s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1174, 10117])).
% 1.86/2.08 tff(10119,plain,
% 1.86/2.08 (~r(z, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1572, 10118, 10111])).
% 1.86/2.08 tff(10120,plain,
% 1.86/2.08 (~r(elem!1, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2440, 10119, 1713])).
% 1.86/2.08 tff(10121,plain,
% 1.86/2.08 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1068, 10120, 1718])).
% 1.86/2.08 tff(10122,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10123,plain,
% 1.86/2.08 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10124,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10123])).
% 1.86/2.08 tff(10125,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[10124, 10122])).
% 1.86/2.08 tff(10126,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(10127,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10126, 10125])).
% 1.86/2.08 tff(10128,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10127, 116, 8086, 10065, 10121, 10108, 10116])).
% 1.86/2.08 tff(10129,plain,((~(z = elem!1)) | (elem!1 = s(z)) | b(s(z), elem!1) | (~b(s(s(z)), elem!1)) | r(z, elem!1) | (s(s(z)) = elem!1) | b(elem!1, z) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(10130,plain,
% 1.86/2.08 (~(z = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10129, 1455, 340, 1331, 1052, 422, 421, 175, 3651, 358])).
% 1.86/2.08 tff(10131,plain,
% 1.86/2.08 (b(z, elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1044, 10130, 1052])).
% 1.86/2.08 tff(10132,plain,
% 1.86/2.08 (~(elem!1 = z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[533, 10130])).
% 1.86/2.08 tff(10133,plain,
% 1.86/2.08 (r(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[545, 10132, 1455])).
% 1.86/2.08 tff(10134,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2824, 10133, 10131, 7113, 5772, 1331, 353, 422, 340])).
% 1.86/2.08 tff(10135,plain,(b(elem!1, z) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | (s(s(z)) = elem!1) | b(s(z), elem!1) | r(z, elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(10136,plain,
% 1.86/2.08 (b(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10135, 1052, 353, 422, 340, 1331, 175, 3651])).
% 1.86/2.08 tff(10137,plain,
% 1.86/2.08 (~b(z, elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8043, 10136, 1331])).
% 1.86/2.08 tff(10138,plain,
% 1.86/2.08 (z = elem!1),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1044, 10137, 1052])).
% 1.86/2.08 tff(10139,plain,
% 1.86/2.08 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10138])).
% 1.86/2.08 tff(10140,plain,
% 1.86/2.08 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.86/2.08 inference(symmetry,[status(thm)],[10139])).
% 1.86/2.08 tff(10141,plain,
% 1.86/2.08 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10140])).
% 1.86/2.08 tff(10142,plain,
% 1.86/2.08 (~b(elem!1, z)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3544, 10141])).
% 1.86/2.08 tff(10143,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10136, 10142])).
% 1.86/2.08 tff(10144,plain,(r(z, elem!1) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | (s(s(z)) = elem!1) | b(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(10145,plain,
% 1.86/2.08 (r(z, elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10144, 422, 353, 1331, 340, 175, 3651])).
% 1.86/2.08 tff(10146,plain,
% 1.86/2.08 (~r(s(z), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[690, 10145, 358])).
% 1.86/2.08 tff(10147,plain,
% 1.86/2.08 (b(s(z), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[210, 10146])).
% 1.86/2.08 tff(10148,plain,
% 1.86/2.08 (~r(z, s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3295, 10145, 358])).
% 1.86/2.08 tff(10149,plain,
% 1.86/2.08 (b(z, s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[289, 10148])).
% 1.86/2.08 tff(10150,plain,
% 1.86/2.08 (~b(s(s(s(z))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3291, 10149, 175, 10147])).
% 1.86/2.08 tff(10151,plain,
% 1.86/2.08 (r(s(s(s(z))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[63, 10150])).
% 1.86/2.08 tff(10152,plain,
% 1.86/2.08 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[279, 254, 270, 271])).
% 1.86/2.08 tff(10153,plain,
% 1.86/2.08 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[325, 10152])).
% 1.86/2.08 tff(10154,plain,
% 1.86/2.08 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[336, 10153, 7782])).
% 1.86/2.08 tff(10155,plain,
% 1.86/2.08 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[149, 10154])).
% 1.86/2.08 tff(10156,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10157,plain,
% 1.86/2.08 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10158,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10157])).
% 1.86/2.08 tff(10159,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[10158, 10156])).
% 1.86/2.08 tff(10160,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(10161,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10160, 10159])).
% 1.86/2.08 tff(10162,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10161, 116, 270, 271, 7113, 10155, 254])).
% 1.86/2.08 tff(10163,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(10164,plain,
% 1.86/2.08 (~b(s(s(s(s(z)))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10163, 10147, 10149])).
% 1.86/2.08 tff(10165,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[247, 10164])).
% 1.86/2.08 tff(10166,plain,
% 1.86/2.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3961, 10165, 10151])).
% 1.86/2.08 tff(10167,plain,
% 1.86/2.08 (~r(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1446, 10147, 358, 10145])).
% 1.86/2.08 tff(10168,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7649, 10149, 10145, 10147, 358])).
% 1.86/2.08 tff(10169,plain,
% 1.86/2.08 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7734, 422])).
% 1.86/2.08 tff(10170,plain,
% 1.86/2.08 (~b(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7661, 271, 1331, 270])).
% 1.86/2.08 tff(10171,plain,
% 1.86/2.08 (r(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[545, 7421, 10170])).
% 1.86/2.08 tff(10172,assumption,(~r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.86/2.08 tff(10173,plain,
% 1.86/2.08 (~r(elem!1, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2671, 228, 10171])).
% 1.86/2.08 tff(10174,plain,
% 1.86/2.08 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1090, 7246])).
% 1.86/2.08 tff(10175,plain,
% 1.86/2.08 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[4415, 10174, 1331, 1049, 3289])).
% 1.86/2.08 tff(10176,plain,
% 1.86/2.08 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.86/2.08 inference(transitivity,[status(thm)],[547, 522])).
% 1.86/2.08 tff(10177,plain,
% 1.86/2.08 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10176])).
% 1.86/2.08 tff(10178,plain,
% 1.86/2.08 (s(s(s(s(z)))) = s(elem!1)),
% 1.86/2.08 inference(transitivity,[status(thm)],[554, 10177, 520])).
% 1.86/2.08 tff(10179,plain,
% 1.86/2.08 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10178])).
% 1.86/2.08 tff(10180,plain,
% 1.86/2.08 (s(s(s(z))) = elem!1),
% 1.86/2.08 inference(transitivity,[status(thm)],[128, 10179, 460])).
% 1.86/2.08 tff(10181,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7258, 10180])).
% 1.86/2.08 tff(10182,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(10183,plain,
% 1.86/2.08 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10182, 521])).
% 1.86/2.08 tff(10184,plain,
% 1.86/2.08 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[885, 10183, 10172])).
% 1.86/2.08 tff(10185,plain,
% 1.86/2.08 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[325, 1735])).
% 1.86/2.08 tff(10186,plain,
% 1.86/2.08 (~(elem!1 = s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[4700, 10185, 340])).
% 1.86/2.08 tff(10187,plain,
% 1.86/2.08 (b(elem!1, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1068, 10186, 1049])).
% 1.86/2.08 tff(10188,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10189,plain,
% 1.86/2.08 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(10190,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[10189])).
% 1.86/2.08 tff(10191,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[10190, 10188])).
% 1.86/2.08 tff(10192,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(10193,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[10192, 10191])).
% 1.86/2.08 tff(10194,plain,
% 1.86/2.08 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[10193, 116, 10187, 1331, 28, 845])).
% 1.86/2.08 tff(10195,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 10194])).
% 1.86/2.08 tff(10196,plain,
% 1.86/2.08 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1584, 10186])).
% 1.86/2.08 tff(10197,plain,
% 1.86/2.08 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1596, 10196, 3289])).
% 1.86/2.08 tff(10198,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10199,plain,
% 1.86/2.09 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10200,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10199])).
% 1.86/2.09 tff(10201,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[10200, 10198])).
% 1.86/2.09 tff(10202,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(10203,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[10202, 10201])).
% 1.86/2.09 tff(10204,plain,
% 1.86/2.09 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10203, 116, 10187, 28, 10197, 845])).
% 1.86/2.09 tff(10205,plain,
% 1.86/2.09 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6694, 10204])).
% 1.86/2.09 tff(10206,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10207,plain,
% 1.86/2.09 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10208,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10207])).
% 1.86/2.09 tff(10209,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[10208, 10206])).
% 1.86/2.09 tff(10210,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(10211,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[10210, 10209])).
% 1.86/2.09 tff(10212,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10211, 77, 328, 10205, 10195])).
% 1.86/2.09 tff(10213,plain,((~r(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))))), elem!1)) | (~b(s(s(z)), elem!1)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | b(s(z), elem!1) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10214,plain,
% 1.86/2.09 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10213, 10184, 1331, 28, 1049, 3289, 340, 156])).
% 1.86/2.09 tff(10215,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[149, 10214, 10175])).
% 1.86/2.09 tff(10216,plain,((~(s(s(elem!1)) = elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | b(s(z), elem!1) | (~r(s(z), s(s(z)))) | r(s(s(s(s(s(z))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10217,plain,
% 1.86/2.09 (~(s(s(elem!1)) = elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10216, 10173, 28, 1331, 3288, 340, 7782, 10172])).
% 1.86/2.09 tff(10218,plain,
% 1.86/2.09 (b(s(s(elem!1)), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[743, 10217, 1373])).
% 1.86/2.09 tff(10219,plain,
% 1.86/2.09 (elem!1 = s(s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7829, 10218, 1331, 7783, 448, 28, 228, 10171, 7423])).
% 1.86/2.09 tff(10220,plain,
% 1.86/2.09 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4700, 10219, 340])).
% 1.86/2.09 tff(10221,plain,
% 1.86/2.09 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[325, 10220])).
% 1.86/2.09 tff(10222,plain,
% 1.86/2.09 (r(elem!1, s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10219])).
% 1.86/2.09 tff(10223,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 1.86/2.09 tff(10224,plain,
% 1.86/2.09 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10219])).
% 1.86/2.09 tff(10225,plain,
% 1.86/2.09 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.09 inference(symmetry,[status(thm)],[10224])).
% 1.86/2.09 tff(10226,plain,
% 1.86/2.09 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10225])).
% 1.86/2.09 tff(10227,plain,
% 1.86/2.09 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6647, 10226])).
% 1.86/2.09 tff(10228,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[885, 10227, 10172])).
% 1.86/2.09 tff(10229,plain,
% 1.86/2.09 (~b(elem!1, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7849, 10228, 10171, 7783, 271, 1331, 28, 10218, 7423, 448, 270])).
% 1.86/2.09 tff(10230,plain,
% 1.86/2.09 (r(elem!1, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6497, 10229, 10223])).
% 1.86/2.09 tff(10231,plain,
% 1.86/2.09 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[10230, 10222])).
% 1.86/2.09 tff(10232,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10233,plain,
% 1.86/2.09 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10234,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10233])).
% 1.86/2.09 tff(10235,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[10234, 10232])).
% 1.86/2.09 tff(10236,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(10237,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[10236, 10235])).
% 1.86/2.09 tff(10238,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10237, 77, 10231, 7782, 10221])).
% 1.86/2.09 tff(10239,plain,((~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(z))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(z), z)) | r(s(s(s(s(s(z))))), elem!1) | b(s(z), elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10240,plain,
% 1.86/2.09 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10239, 10165, 10169, 10149, 1331, 7148, 10145, 10147, 10168, 340, 10167])).
% 1.86/2.09 tff(10241,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3951, 10240, 10166])).
% 1.86/2.09 tff(10242,plain,((s(s(z)) = elem!1) | (~b(s(s(z)), elem!1)) | b(s(z), elem!1) | (~b(s(z), s(s(s(z))))) | (s(z) = elem!1) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10243,plain,
% 1.86/2.09 (s(s(z)) = elem!1),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10242, 9711, 340, 8278, 9712, 7120])).
% 1.86/2.09 tff(10244,plain,
% 1.86/2.09 (b(s(s(z)), elem!1) <=> b(elem!1, elem!1)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10243])).
% 1.86/2.09 tff(10245,plain,
% 1.86/2.09 (b(elem!1, elem!1) <=> b(s(s(z)), elem!1)),
% 1.86/2.09 inference(symmetry,[status(thm)],[10244])).
% 1.86/2.09 tff(10246,plain,
% 1.86/2.09 ((~b(elem!1, elem!1)) <=> (~b(s(s(z)), elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10245])).
% 1.86/2.09 tff(10247,plain,
% 1.86/2.09 (~b(s(s(z)), elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3544, 10246])).
% 1.86/2.09 tff(10248,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[9711, 10247])).
% 1.86/2.09 tff(10249,plain,(b(s(z), elem!1) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10250,plain,
% 1.86/2.09 (b(s(z), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10249, 4432])).
% 1.86/2.09 tff(10251,plain,
% 1.86/2.09 (~r(s(s(s(z))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2136, 67, 155])).
% 1.86/2.09 tff(10252,plain,
% 1.86/2.09 (b(s(s(s(z))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[402, 21, 135, 10251])).
% 1.86/2.09 tff(10253,plain,
% 1.86/2.09 (~r(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7122, 67, 155])).
% 1.86/2.09 tff(10254,plain,
% 1.86/2.09 (b(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[194, 10253])).
% 1.86/2.09 tff(10255,plain,
% 1.86/2.09 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8864, 228, 155])).
% 1.86/2.09 tff(10256,plain,
% 1.86/2.09 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[325, 10255])).
% 1.86/2.09 tff(10257,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10258,plain,
% 1.86/2.09 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10259,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10258])).
% 1.86/2.09 tff(10260,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[10259, 10257])).
% 1.86/2.09 tff(10261,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(10262,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[10261, 10260])).
% 1.86/2.09 tff(10263,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10262, 116, 847, 8775, 10254, 10252, 10256])).
% 1.86/2.09 tff(10264,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10265,plain,
% 1.86/2.09 (~r(s(s(s(s(z)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10264, 67, 847, 155])).
% 1.86/2.09 tff(10266,plain,
% 1.86/2.09 (b(s(s(s(s(z)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[247, 10265])).
% 1.86/2.09 tff(10267,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 1.86/2.09 tff(10268,plain,
% 1.86/2.09 (s(s(s(z))) = z),
% 1.86/2.09 inference(symmetry,[status(thm)],[10267])).
% 1.86/2.09 tff(10269,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[59, 10268])).
% 1.86/2.09 tff(10270,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10271,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2681, 77, 155, 1212, 156])).
% 1.86/2.09 tff(10272,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10273,plain,
% 1.86/2.09 (~r(s(z), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10272, 1212, 155])).
% 1.86/2.09 tff(10274,plain,
% 1.86/2.09 (b(s(z), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[172, 10273])).
% 1.86/2.09 tff(10275,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10276,plain,
% 1.86/2.09 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10277,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10276])).
% 1.86/2.09 tff(10278,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[10277, 10275])).
% 1.86/2.09 tff(10279,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(10280,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[10279, 10278])).
% 1.86/2.09 tff(10281,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10280, 116, 847, 27, 175, 174, 8631])).
% 1.86/2.09 tff(10282,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(10283,plain,
% 1.86/2.09 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10282, 10274, 10254, 847, 10252])).
% 1.86/2.09 tff(10284,plain,
% 1.86/2.09 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[105, 10283])).
% 1.86/2.09 tff(10285,plain,
% 1.86/2.09 (~r(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[9352, 10284, 1212])).
% 1.86/2.09 tff(10286,plain,
% 1.86/2.09 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10282, 174, 175, 847, 8631])).
% 1.86/2.09 tff(10287,plain,
% 1.86/2.09 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[105, 10286])).
% 1.86/2.09 tff(10288,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5016, 3953, 10287])).
% 1.86/2.09 tff(10289,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10290,plain,
% 1.86/2.09 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10291,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(s(s(z)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[10290])).
% 1.86/2.09 tff(10292,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(s(s(z))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[10291, 10289])).
% 1.86/2.09 tff(10293,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(10294,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[10293, 10292])).
% 1.86/2.09 tff(10295,plain,
% 1.86/2.09 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10294, 116, 847, 175, 10288, 8631])).
% 1.86/2.09 tff(10296,plain,
% 1.86/2.09 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5816, 21, 10295])).
% 1.86/2.09 tff(10297,plain,
% 1.86/2.09 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[10296, 5783])).
% 1.86/2.09 tff(10298,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(10299,plain,
% 1.86/2.09 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10300,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10299])).
% 1.86/2.10 tff(10301,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10300, 10298])).
% 1.86/2.10 tff(10302,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10303,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10302, 10301])).
% 1.86/2.10 tff(10304,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10303, 77, 10287, 3651, 10297])).
% 1.86/2.10 tff(10305,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 10304])).
% 1.86/2.10 tff(10306,plain,
% 1.86/2.10 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5006, 77, 10287, 3953])).
% 1.86/2.10 tff(10307,plain,
% 1.86/2.10 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[149, 10306])).
% 1.86/2.10 tff(10308,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4984, 77, 10287, 3953])).
% 1.86/2.10 tff(10309,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[226, 10308])).
% 1.86/2.10 tff(10310,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6541, 116, 10309, 10307, 174])).
% 1.86/2.10 tff(10311,plain,
% 1.86/2.10 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2054, 21, 10310])).
% 1.86/2.10 tff(10312,plain,
% 1.86/2.10 (r(s(s(s(s(z)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10311, 2044])).
% 1.86/2.10 tff(10313,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10314,plain,
% 1.86/2.10 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10315,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10314])).
% 1.86/2.10 tff(10316,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10315, 10313])).
% 1.86/2.10 tff(10317,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10318,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10317, 10316])).
% 1.86/2.10 tff(10319,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10318, 77, 10312, 10297])).
% 1.86/2.10 tff(10320,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6694, 10319])).
% 1.86/2.10 tff(10321,plain,
% 1.86/2.10 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10322,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10321])).
% 1.86/2.10 tff(10323,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10322, 7019])).
% 1.86/2.10 tff(10324,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10325,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10324, 10323])).
% 1.86/2.10 tff(10326,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10325, 116, 10309, 10307, 10320, 10305])).
% 1.86/2.10 tff(10327,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(10328,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10327, 10274, 3651, 847, 10254, 10252])).
% 1.86/2.10 tff(10329,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3951, 10328])).
% 1.86/2.10 tff(10330,plain,
% 1.86/2.10 (~r(z, s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8970, 10329, 10254, 10284, 7113, 155, 67])).
% 1.86/2.10 tff(10331,plain,
% 1.86/2.10 (b(z, s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[289, 10330])).
% 1.86/2.10 tff(10332,plain,
% 1.86/2.10 (~b(z, s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[9363, 10331, 10252, 10254])).
% 1.86/2.10 tff(10333,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[267, 21, 10332, 10285, 10270])).
% 1.86/2.10 tff(10334,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(10335,plain,
% 1.86/2.10 (~r(z, s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10334, 67, 155, 3651, 847])).
% 1.86/2.10 tff(10336,plain,
% 1.86/2.10 (b(z, s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1174, 10335])).
% 1.86/2.10 tff(10337,plain,
% 1.86/2.10 (~b(s(z), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10282, 27, 175, 847, 8631])).
% 1.86/2.10 tff(10338,plain,
% 1.86/2.10 (r(s(z), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[172, 10337])).
% 1.86/2.10 tff(10339,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10340,plain,
% 1.86/2.10 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10341,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10340])).
% 1.86/2.10 tff(10342,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10341, 10339])).
% 1.86/2.10 tff(10343,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10344,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10343, 10342])).
% 1.86/2.10 tff(10345,plain,
% 1.86/2.10 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10344, 116, 847, 27, 28, 8631])).
% 1.86/2.10 tff(10346,plain,
% 1.86/2.10 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[149, 10345])).
% 1.86/2.10 tff(10347,plain,
% 1.86/2.10 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10262, 116, 847, 28, 175, 8631])).
% 1.86/2.10 tff(10348,plain,
% 1.86/2.10 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[325, 10347])).
% 1.86/2.10 tff(10349,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[336, 10348, 10346, 10338])).
% 1.86/2.10 tff(10350,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(10351,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10350, 27, 175, 8631, 847])).
% 1.86/2.10 tff(10352,plain,
% 1.86/2.10 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3951, 10351])).
% 1.86/2.10 tff(10353,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10354,plain,
% 1.86/2.10 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10355,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10354])).
% 1.86/2.10 tff(10356,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10355, 10353])).
% 1.86/2.10 tff(10357,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10358,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10357, 10356])).
% 1.86/2.10 tff(10359,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10358, 116, 7113, 2442, 254])).
% 1.86/2.10 tff(10360,plain,
% 1.86/2.10 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[226, 10359])).
% 1.86/2.10 tff(10361,plain,
% 1.86/2.10 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5905, 10360, 10352])).
% 1.86/2.10 tff(10362,plain,
% 1.86/2.10 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[89, 21, 10361, 56])).
% 1.86/2.10 tff(10363,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10364,plain,
% 1.86/2.10 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10365,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10364])).
% 1.86/2.10 tff(10366,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10365, 10363])).
% 1.86/2.10 tff(10367,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10368,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10367, 10366])).
% 1.86/2.10 tff(10369,plain,
% 1.86/2.10 (~b(z, s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10368, 116, 7113, 2442, 10362])).
% 1.86/2.10 tff(10370,plain,
% 1.86/2.10 (r(z, s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[267, 21, 10369, 10270])).
% 1.86/2.10 tff(10371,plain,
% 1.86/2.10 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6403, 10362, 175, 27])).
% 1.86/2.10 tff(10372,plain,
% 1.86/2.10 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1380, 10371])).
% 1.86/2.10 tff(10373,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10374,plain,
% 1.86/2.10 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10375,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10374])).
% 1.86/2.10 tff(10376,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10375, 10373])).
% 1.86/2.10 tff(10377,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10378,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10377, 10376])).
% 1.86/2.10 tff(10379,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10378, 77, 10372, 10370])).
% 1.86/2.10 tff(10380,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[898, 21, 895, 10379])).
% 1.86/2.10 tff(10381,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10382,plain,
% 1.86/2.10 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(10383,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[10382])).
% 1.86/2.10 tff(10384,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[10383, 10381])).
% 1.86/2.10 tff(10385,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(10386,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[10385, 10384])).
% 1.86/2.10 tff(10387,plain,
% 1.86/2.10 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[10386, 77, 10360, 10352, 10372])).
% 1.86/2.10 tff(10388,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6694, 10387])).
% 1.86/2.10 tff(10389,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10390,plain,
% 1.86/2.11 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10391,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[10390])).
% 1.86/2.11 tff(10392,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[10391, 10389])).
% 1.86/2.11 tff(10393,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(10394,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[10393, 10392])).
% 1.86/2.11 tff(10395,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10394, 116, 7113, 2442, 254, 10388, 10380])).
% 1.86/2.11 tff(10396,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(10397,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10396, 10336, 10266, 10254, 10252, 847])).
% 1.86/2.11 tff(10398,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[105, 10397])).
% 1.86/2.11 tff(10399,plain,
% 1.86/2.11 (~r(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8970, 28, 10254, 2235, 7113, 155, 67])).
% 1.86/2.11 tff(10400,plain,
% 1.86/2.11 (b(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[289, 10399])).
% 1.86/2.11 tff(10401,plain,
% 1.86/2.11 (~b(s(z), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[9348, 10400, 7113, 2442])).
% 1.86/2.11 tff(10402,plain,
% 1.86/2.11 (~r(s(z), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[9298, 10400, 7113, 155, 67, 10254, 28])).
% 1.86/2.11 tff(10403,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[172, 10402, 10401])).
% 1.86/2.11 tff(10404,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(10405,plain,
% 1.86/2.11 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10404, 67, 155, 10336, 10398])).
% 1.86/2.11 tff(10406,plain,
% 1.86/2.11 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3951, 10405])).
% 1.86/2.11 tff(10407,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10408,plain,
% 1.86/2.11 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10409,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[10408])).
% 1.86/2.11 tff(10410,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[10409, 10407])).
% 1.86/2.11 tff(10411,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(10412,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[10411, 10410])).
% 1.86/2.11 tff(10413,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10412, 116, 7113, 10336, 10266])).
% 1.86/2.11 tff(10414,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[149, 10413])).
% 1.86/2.11 tff(10415,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5006, 77, 10398, 10414, 10406])).
% 1.86/2.11 tff(10416,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(10417,plain,
% 1.86/2.11 (~r(s(s(s(z))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10416, 155, 847, 3651])).
% 1.86/2.11 tff(10418,plain,
% 1.86/2.11 (b(s(s(s(z))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[63, 10417])).
% 1.86/2.11 tff(10419,plain,
% 1.86/2.11 (~b(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8127, 27, 7113, 2247])).
% 1.86/2.11 tff(10420,plain,
% 1.86/2.11 (r(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1174, 10419])).
% 1.86/2.11 tff(10421,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7875, 77, 293, 1212, 3651])).
% 1.86/2.11 tff(10422,plain,((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(10423,plain,
% 1.86/2.11 (~r(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10422, 10420, 3651])).
% 1.86/2.11 tff(10424,plain,
% 1.86/2.11 (b(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[289, 10423])).
% 1.86/2.11 tff(10425,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10426,plain,
% 1.86/2.11 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10427,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[10426])).
% 1.86/2.11 tff(10428,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[10427, 10425])).
% 1.86/2.11 tff(10429,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(10430,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[10429, 10428])).
% 1.86/2.11 tff(10431,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10430, 116, 847, 10424, 2247, 7113, 27])).
% 1.86/2.11 tff(10432,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(10433,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10432, 10418, 847, 3651])).
% 1.86/2.11 tff(10434,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[105, 10433])).
% 1.86/2.11 tff(10435,plain,
% 1.86/2.11 (~r(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8072, 10434, 155, 3651])).
% 1.86/2.11 tff(10436,plain,
% 1.86/2.11 (b(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[194, 10435])).
% 1.86/2.11 tff(10437,plain,
% 1.86/2.11 (~r(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[9352, 1212, 2235])).
% 1.86/2.11 tff(10438,plain,
% 1.86/2.11 (b(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[267, 21, 10437, 10270])).
% 1.86/2.11 tff(10439,plain,
% 1.86/2.11 (~r(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10422, 1212, 3651])).
% 1.86/2.11 tff(10440,plain,
% 1.86/2.11 (b(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[289, 10439])).
% 1.86/2.11 tff(10441,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6529, 116, 10440, 2247, 10438, 175])).
% 1.86/2.11 tff(10442,plain,((~r(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(10443,plain,
% 1.86/2.11 (~r(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10442, 10418, 10436, 10434, 3651])).
% 1.86/2.11 tff(10444,plain,
% 1.86/2.11 (b(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1174, 10443])).
% 1.86/2.11 tff(10445,plain,
% 1.86/2.11 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2801, 116, 2247, 28, 2442, 175])).
% 1.86/2.11 tff(10446,plain,
% 1.86/2.11 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[325, 10445])).
% 1.86/2.11 tff(10447,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8864, 10446, 155])).
% 1.86/2.11 tff(10448,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[247, 10447])).
% 1.86/2.11 tff(10449,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2450, 10448, 2247, 2442, 28])).
% 1.86/2.11 tff(10450,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[149, 10449])).
% 1.86/2.11 tff(10451,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[383, 77, 10450, 10446, 3651])).
% 1.86/2.11 tff(10452,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(10453,plain,
% 1.86/2.11 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10452, 10418, 3651, 10444, 155, 10436])).
% 1.86/2.11 tff(10454,plain,
% 1.86/2.11 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3951, 10453])).
% 1.86/2.11 tff(10455,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5016, 10454, 10434])).
% 1.86/2.11 tff(10456,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10457,plain,
% 1.86/2.11 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10458,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[10457])).
% 1.86/2.11 tff(10459,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[10458, 10456])).
% 1.86/2.11 tff(10460,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(10461,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[10460, 10459])).
% 1.86/2.11 tff(10462,plain,
% 1.86/2.11 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10461, 116, 10418, 10444, 10436, 10455])).
% 1.86/2.11 tff(10463,plain,
% 1.86/2.11 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5816, 21, 10462])).
% 1.86/2.11 tff(10464,plain,
% 1.86/2.11 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10463, 5783])).
% 1.86/2.11 tff(10465,plain,
% 1.86/2.11 (~r(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8072, 2235, 155, 3651])).
% 1.86/2.11 tff(10466,plain,
% 1.86/2.11 (b(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[194, 10465])).
% 1.86/2.11 tff(10467,plain,
% 1.86/2.11 (~r(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10442, 2247, 175, 2235, 3651])).
% 1.86/2.11 tff(10468,plain,
% 1.86/2.11 (b(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1174, 10467])).
% 1.86/2.11 tff(10469,plain,
% 1.86/2.11 (~b(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2791, 116, 2247, 7113, 10468])).
% 1.86/2.11 tff(10470,plain,
% 1.86/2.11 (r(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[89, 21, 10469, 56])).
% 1.86/2.11 tff(10471,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5905, 3953, 10470])).
% 1.86/2.11 tff(10472,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[226, 10471])).
% 1.86/2.11 tff(10473,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10474,plain,
% 1.86/2.11 (((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10475,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[10474])).
% 1.86/2.11 tff(10476,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[10475, 10473])).
% 1.86/2.11 tff(10477,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(10478,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[10477, 10476])).
% 1.86/2.11 tff(10479,plain,
% 1.86/2.11 (~b(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10478, 116, 271, 10472, 7113, 10468])).
% 1.86/2.11 tff(10480,plain,
% 1.86/2.11 (r(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1576, 21, 10479, 1563])).
% 1.86/2.11 tff(10481,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5016, 3953, 2235])).
% 1.86/2.11 tff(10482,plain,
% 1.86/2.11 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7007, 116, 271, 2247, 175, 10481])).
% 1.86/2.11 tff(10483,plain,
% 1.86/2.11 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5816, 21, 10482])).
% 1.86/2.11 tff(10484,plain,
% 1.86/2.11 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10483, 5783])).
% 1.86/2.11 tff(10485,plain,
% 1.86/2.11 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10303, 77, 2235, 3651, 10484])).
% 1.86/2.11 tff(10486,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 10485])).
% 1.86/2.11 tff(10487,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10488,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(10489,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[10488, 10487])).
% 1.86/2.11 tff(10490,plain,
% 1.86/2.11 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[10489, 116, 271, 10472, 7113, 10486])).
% 1.86/2.11 tff(10491,plain,
% 1.86/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6694, 10490])).
% 1.86/2.11 tff(10492,plain,
% 1.86/2.11 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6701, 77, 10491, 10480])).
% 1.86/2.11 tff(10493,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10494,plain,
% 1.86/2.11 (((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(10495,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[10494])).
% 1.86/2.11 tff(10496,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10495, 10493])).
% 1.86/2.12 tff(10497,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(10498,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[10497, 10496])).
% 1.86/2.12 tff(10499,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10498, 116, 271, 7113, 10468, 10486])).
% 1.86/2.12 tff(10500,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[898, 21, 895, 10499, 10492])).
% 1.86/2.12 tff(10501,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(10502,plain,
% 1.86/2.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10501, 271, 2235, 3651, 2247, 10466])).
% 1.86/2.12 tff(10503,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3951, 10502])).
% 1.86/2.12 tff(10504,plain,
% 1.86/2.12 (~r(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10442, 2247, 10466, 2235, 3651])).
% 1.86/2.12 tff(10505,plain,
% 1.86/2.12 (b(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1174, 10504])).
% 1.86/2.12 tff(10506,plain,
% 1.86/2.12 (~b(s(z), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[9348, 271, 7113, 10505])).
% 1.86/2.12 tff(10507,plain,
% 1.86/2.12 (r(s(z), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[172, 10506])).
% 1.86/2.12 tff(10508,plain,
% 1.86/2.12 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2803, 10503, 7113, 2247, 10507, 10505])).
% 1.86/2.12 tff(10509,plain,
% 1.86/2.12 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[325, 10508])).
% 1.86/2.12 tff(10510,plain,
% 1.86/2.12 (~r(s(s(s(s(z)))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8864, 10509, 155])).
% 1.86/2.12 tff(10511,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[247, 10510])).
% 1.86/2.12 tff(10512,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[336, 10509, 10507])).
% 1.86/2.12 tff(10513,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[149, 10512])).
% 1.86/2.12 tff(10514,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2450, 10513, 10511, 2247, 10505, 10503])).
% 1.86/2.12 tff(10515,plain,((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(10516,plain,
% 1.86/2.12 (~b(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10515, 10418, 155, 10434, 3651])).
% 1.86/2.12 tff(10517,plain,
% 1.86/2.12 (r(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[289, 10516])).
% 1.86/2.12 tff(10518,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[5835, 77, 10517, 10464])).
% 1.86/2.12 tff(10519,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[898, 21, 895, 10518])).
% 1.86/2.12 tff(10520,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10521,plain,
% 1.86/2.12 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10522,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[10521])).
% 1.86/2.12 tff(10523,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10522, 10520])).
% 1.86/2.12 tff(10524,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(10525,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[10524, 10523])).
% 1.86/2.12 tff(10526,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10525, 116, 10418, 7113, 10444, 10455, 10519])).
% 1.86/2.12 tff(10527,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(10528,plain,
% 1.86/2.12 (~r(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10527, 3651, 847])).
% 1.86/2.12 tff(10529,plain,
% 1.86/2.12 (b(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[210, 10528])).
% 1.86/2.12 tff(10530,plain,
% 1.86/2.12 (~b(s(s(s(s(z)))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10163, 10440, 10529])).
% 1.86/2.12 tff(10531,plain,
% 1.86/2.12 (r(s(s(s(s(z)))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[247, 10530])).
% 1.86/2.12 tff(10532,plain,
% 1.86/2.12 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.86/2.12 inference(commutativity,[status(thm)],[])).
% 1.86/2.12 tff(10533,plain,
% 1.86/2.12 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.12 inference(symmetry,[status(thm)],[10532])).
% 1.86/2.12 tff(10534,plain,
% 1.86/2.12 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(z)))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[10533])).
% 1.86/2.12 tff(10535,plain,
% 1.86/2.12 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[1138, 10534])).
% 1.86/2.12 tff(10536,plain,
% 1.86/2.12 (b(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6442, 1713, 847])).
% 1.86/2.12 tff(10537,plain,
% 1.86/2.12 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[442])).
% 1.86/2.12 tff(10538,plain,
% 1.86/2.12 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.86/2.12 inference(symmetry,[status(thm)],[10537])).
% 1.86/2.12 tff(10539,plain,
% 1.86/2.12 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10002, 10001, 10538])).
% 1.86/2.12 tff(10540,plain,
% 1.86/2.12 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10052, 10051])).
% 1.86/2.12 tff(10541,plain,
% 1.86/2.12 (r(elem!1, s(s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[1212, 10540])).
% 1.86/2.12 tff(10542,plain,
% 1.86/2.12 (~r(elem!1, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[802, 10541, 794])).
% 1.86/2.12 tff(10543,plain,
% 1.86/2.12 (b(elem!1, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[633, 10542, 3670])).
% 1.86/2.12 tff(10544,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6926, 10543, 847, 1955, 794, 8086])).
% 1.86/2.12 tff(10545,plain,
% 1.86/2.12 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[885, 10544, 1896])).
% 1.86/2.12 tff(10546,plain,
% 1.86/2.12 (r(s(s(s(z))), elem!1)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[67, 9722])).
% 1.86/2.12 tff(10547,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6283, 77, 10546, 10545])).
% 1.86/2.12 tff(10548,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1380, 10547])).
% 1.86/2.12 tff(10549,plain,
% 1.86/2.12 (r(z, s(s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[1212, 10053])).
% 1.86/2.12 tff(10550,plain,
% 1.86/2.12 (~r(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3185, 10549, 794])).
% 1.86/2.12 tff(10551,plain,
% 1.86/2.12 (b(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[289, 10550])).
% 1.86/2.12 tff(10552,plain,
% 1.86/2.12 (~b(s(s(s(s(z)))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10163, 10551, 10536])).
% 1.86/2.12 tff(10553,plain,
% 1.86/2.12 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3582, 10552, 1713])).
% 1.86/2.12 tff(10554,plain,
% 1.86/2.12 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1596, 10553, 3578])).
% 1.86/2.12 tff(10555,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10556,plain,
% 1.86/2.12 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10557,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[10556])).
% 1.86/2.12 tff(10558,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10557, 10555])).
% 1.86/2.12 tff(10559,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(10560,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[10559, 10558])).
% 1.86/2.12 tff(10561,plain,
% 1.86/2.12 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10560, 77, 10554, 10545])).
% 1.86/2.12 tff(10562,plain,
% 1.86/2.12 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6694, 10561])).
% 1.86/2.12 tff(10563,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10564,plain,
% 1.86/2.12 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10565,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[10564])).
% 1.86/2.12 tff(10566,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10565, 10563])).
% 1.86/2.12 tff(10567,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(10568,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[10567, 10566])).
% 1.86/2.12 tff(10569,plain,
% 1.86/2.12 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10568, 77, 10546, 10554])).
% 1.86/2.12 tff(10570,plain,
% 1.86/2.12 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1146, 10569])).
% 1.86/2.12 tff(10571,plain,
% 1.86/2.12 (r(s(s(s(s(z)))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[247, 10552])).
% 1.86/2.12 tff(10572,plain,
% 1.86/2.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3961, 10571, 67])).
% 1.86/2.12 tff(10573,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3951, 10572])).
% 1.86/2.12 tff(10574,plain,
% 1.86/2.12 (((~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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10575,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[10574])).
% 1.86/2.12 tff(10576,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10575, 8927])).
% 1.86/2.12 tff(10577,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(10578,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[10577, 10576])).
% 1.86/2.12 tff(10579,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10578, 116, 10573, 10570, 10562, 10548])).
% 1.86/2.12 tff(10580,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(10581,plain,
% 1.86/2.12 (~r(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10580, 67, 847, 794, 442])).
% 1.86/2.12 tff(10582,plain,
% 1.86/2.12 (b(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1174, 10581])).
% 1.86/2.12 tff(10583,plain,
% 1.86/2.12 (b(z, s(s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[10582, 10539])).
% 1.86/2.12 tff(10584,plain,
% 1.86/2.12 ((~b(s(s(s(s(s(z))))), z)) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[986, 1901])).
% 1.86/2.12 tff(10585,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10584, 10583, 10536, 8085, 1955, 8086])).
% 1.86/2.12 tff(10586,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4869, 10585, 1713])).
% 1.86/2.12 tff(10587,plain,
% 1.86/2.12 (r(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[885, 10586, 1896])).
% 1.86/2.12 tff(10588,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10589,plain,
% 1.86/2.12 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(10590,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[10589])).
% 1.86/2.12 tff(10591,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[10590, 10588])).
% 1.86/2.12 tff(10592,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(10593,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[10592, 10591])).
% 1.86/2.12 tff(10594,plain,
% 1.86/2.12 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[10593, 77, 10546, 10587])).
% 1.86/2.12 tff(10595,plain,
% 1.86/2.12 (((~![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)))))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(10596,plain,
% 1.96/2.12 ((~![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)))))))),
% 1.96/2.12 inference(quant_inst,[status(thm)],[])).
% 1.96/2.12 tff(10597,plain,
% 1.96/2.12 ((~![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))))))),
% 1.96/2.12 inference(modus_ponens,[status(thm)],[10596, 10595])).
% 1.96/2.12 tff(10598,plain,
% 1.96/2.12 ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[10597, 21, 10594])).
% 1.96/2.12 tff(10599,plain,
% 1.96/2.12 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[10598, 10535])).
% 1.96/2.12 tff(10600,plain,
% 1.96/2.12 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[6283, 77, 10546, 10587])).
% 1.96/2.12 tff(10601,plain,
% 1.96/2.12 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[1380, 10600])).
% 1.96/2.12 tff(10602,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.96/2.12 tff(10603,plain,
% 1.96/2.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[3961, 3552, 67])).
% 1.96/2.12 tff(10604,plain,
% 1.96/2.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[3951, 10603])).
% 1.96/2.12 tff(10605,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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))))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(10606,plain,
% 1.96/2.12 (((~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(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(s(z))))), 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))))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(10607,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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)))))))),
% 1.96/2.12 inference(monotonicity,[status(thm)],[10606])).
% 1.96/2.12 tff(10608,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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))))))),
% 1.96/2.12 inference(transitivity,[status(thm)],[10607, 10605])).
% 1.96/2.12 tff(10609,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.12 inference(quant_inst,[status(thm)],[])).
% 1.96/2.12 tff(10610,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.96/2.12 inference(modus_ponens,[status(thm)],[10609, 10608])).
% 1.96/2.12 tff(10611,plain,
% 1.96/2.12 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[10610, 116, 10604, 5031, 10602])).
% 1.96/2.12 tff(10612,plain,
% 1.96/2.12 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[3582, 239, 404])).
% 1.96/2.12 tff(10613,plain,
% 1.96/2.12 (r(s(s(s(s(z)))), elem!1)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[1596, 10612, 2640])).
% 1.96/2.12 tff(10614,plain,
% 1.96/2.12 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[10560, 77, 10613, 1027])).
% 1.96/2.12 tff(10615,plain,
% 1.96/2.12 ($false),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[6694, 10614, 10611])).
% 1.96/2.13 tff(10616,plain,(b(s(s(s(s(z)))), z) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), z)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(10617,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10616, 10587, 10601, 10599, 3578, 67, 1713])).
% 1.96/2.13 tff(10618,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10617, 1719])).
% 1.96/2.13 tff(10619,plain,
% 1.96/2.13 (b(s(elem!1), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6119, 442, 847])).
% 1.96/2.13 tff(10620,plain,
% 1.96/2.13 (b(elem!1, s(s(elem!1)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10582, 10003])).
% 1.96/2.13 tff(10621,plain,
% 1.96/2.13 (~b(s(elem!1), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3388, 116, 8086, 10620, 10619])).
% 1.96/2.13 tff(10622,plain,
% 1.96/2.13 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1836, 21, 10621])).
% 1.96/2.13 tff(10623,plain,
% 1.96/2.13 (r(s(elem!1), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10622, 1823])).
% 1.96/2.13 tff(10624,plain,
% 1.96/2.13 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3377, 10617, 8085, 10583])).
% 1.96/2.13 tff(10625,plain,
% 1.96/2.13 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3559, 10624, 1713])).
% 1.96/2.13 tff(10626,plain,
% 1.96/2.13 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[226, 10625])).
% 1.96/2.13 tff(10627,plain,
% 1.96/2.13 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10626, 1855])).
% 1.96/2.13 tff(10628,plain,
% 1.96/2.13 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8996, 77, 10627, 10623])).
% 1.96/2.13 tff(10629,plain,
% 1.96/2.13 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1776, 21, 10628])).
% 1.96/2.13 tff(10630,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10629, 1757])).
% 1.96/2.13 tff(10631,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10632,plain,
% 1.96/2.13 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10633,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[10632])).
% 1.96/2.13 tff(10634,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.96/2.13 inference(transitivity,[status(thm)],[10633, 10631])).
% 1.96/2.13 tff(10635,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(10636,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10635, 10634])).
% 1.96/2.13 tff(10637,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10636, 116, 616, 1879, 846, 7355, 1725])).
% 1.96/2.13 tff(10638,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(10639,plain,
% 1.96/2.13 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10638, 10620, 8086, 10619, 10630])).
% 1.96/2.13 tff(10640,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10639, 10618])).
% 1.96/2.13 tff(10641,plain,((~r(s(s(s(z))), z)) | (~(z = elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(10642,plain,
% 1.96/2.13 (~r(s(s(s(z))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10641, 442, 847, 9717])).
% 1.96/2.13 tff(10643,plain,
% 1.96/2.13 (b(s(s(s(z))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[63, 10642])).
% 1.96/2.13 tff(10644,plain,
% 1.96/2.13 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.96/2.13 inference(symmetry,[status(thm)],[10002])).
% 1.96/2.13 tff(10645,plain,
% 1.96/2.13 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.96/2.13 inference(symmetry,[status(thm)],[10001])).
% 1.96/2.13 tff(10646,plain,
% 1.96/2.13 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.96/2.13 inference(transitivity,[status(thm)],[10537, 10645, 10644])).
% 1.96/2.13 tff(10647,plain,
% 1.96/2.13 (~b(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2936, 271, 7113, 270, 2247])).
% 1.96/2.13 tff(10648,plain,
% 1.96/2.13 (r(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[105, 10647])).
% 1.96/2.13 tff(10649,plain,
% 1.96/2.13 (~b(s(z), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3291, 271, 270, 2247])).
% 1.96/2.13 tff(10650,plain,
% 1.96/2.13 (r(s(z), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[194, 10649])).
% 1.96/2.13 tff(10651,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[7144, 10650, 10648, 7113, 271])).
% 1.96/2.13 tff(10652,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(10653,plain,
% 1.96/2.13 (~b(z, s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10652, 10536, 10643])).
% 1.96/2.13 tff(10654,plain,
% 1.96/2.13 (r(z, s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[289, 10653])).
% 1.96/2.13 tff(10655,plain,
% 1.96/2.13 (~r(z, s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3185, 10654, 9717])).
% 1.96/2.13 tff(10656,plain,
% 1.96/2.13 (b(z, s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[514, 10655])).
% 1.96/2.13 tff(10657,plain,
% 1.96/2.13 (b(z, s(s(z)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10656, 10646])).
% 1.96/2.13 tff(10658,plain,
% 1.96/2.13 (~b(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8127, 10657, 7113, 10643])).
% 1.96/2.13 tff(10659,plain,
% 1.96/2.13 (r(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[105, 10658])).
% 1.96/2.13 tff(10660,plain,
% 1.96/2.13 (r(s(s(elem!1)), s(elem!1))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3651, 9715])).
% 1.96/2.13 tff(10661,plain,
% 1.96/2.13 (b(s(s(s(z))), elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10643, 3547])).
% 1.96/2.13 tff(10662,plain,
% 1.96/2.13 (b(elem!1, s(s(elem!1)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10656, 10537])).
% 1.96/2.13 tff(10663,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10664,plain,
% 1.96/2.13 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10665,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[10664])).
% 1.96/2.13 tff(10666,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[10665, 10663])).
% 1.96/2.13 tff(10667,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(10668,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10667, 10666])).
% 1.96/2.13 tff(10669,plain,
% 1.96/2.13 (~b(s(s(s(z))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10668, 116, 8086, 10662, 10661, 10619])).
% 1.96/2.13 tff(10670,plain,
% 1.96/2.13 (r(s(s(s(z))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1853, 10669, 1783])).
% 1.96/2.13 tff(10671,plain,
% 1.96/2.13 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2617, 10670, 10660])).
% 1.96/2.13 tff(10672,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2605, 10671, 10659, 442])).
% 1.96/2.13 tff(10673,plain,((~(z = elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(10674,plain,
% 1.96/2.13 (~(z = elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10673, 847, 3651])).
% 1.96/2.13 tff(10675,plain,
% 1.96/2.13 (~(elem!1 = z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[533, 10674])).
% 1.96/2.13 tff(10676,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10677,plain,
% 1.96/2.13 (((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10678,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[10677])).
% 1.96/2.13 tff(10679,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[10678, 10676])).
% 1.96/2.13 tff(10680,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(10681,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10680, 10679])).
% 1.96/2.13 tff(10682,plain,
% 1.96/2.13 (~b(s(z), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10681, 116, 847, 10529, 10440, 7113])).
% 1.96/2.13 tff(10683,plain,
% 1.96/2.13 (~(s(s(z)) = elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2038, 10682, 847])).
% 1.96/2.13 tff(10684,plain,
% 1.96/2.13 (~b(s(s(s(z))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10652, 10440, 10529])).
% 1.96/2.13 tff(10685,plain,
% 1.96/2.13 (r(s(s(s(z))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[63, 10684])).
% 1.96/2.13 tff(10686,plain,
% 1.96/2.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3961, 10685, 10531])).
% 1.96/2.13 tff(10687,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3951, 10686])).
% 1.96/2.13 tff(10688,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10689,plain,
% 1.96/2.13 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10690,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[10689])).
% 1.96/2.13 tff(10691,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[10690, 10688])).
% 1.96/2.13 tff(10692,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(10693,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10692, 10691])).
% 1.96/2.13 tff(10694,plain,
% 1.96/2.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10693, 77, 67, 228])).
% 1.96/2.13 tff(10695,plain,
% 1.96/2.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1146, 10694])).
% 1.96/2.13 tff(10696,plain,
% 1.96/2.13 (~b(s(z), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6099, 293, 847, 1052, 518])).
% 1.96/2.13 tff(10697,plain,
% 1.96/2.13 (r(s(z), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[210, 10696])).
% 1.96/2.13 tff(10698,plain,
% 1.96/2.13 (~r(s(s(s(z))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2136, 10697, 67])).
% 1.96/2.13 tff(10699,plain,
% 1.96/2.13 (b(s(s(s(z))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[402, 21, 135, 10698])).
% 1.96/2.13 tff(10700,plain,
% 1.96/2.13 (~r(s(z), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[7122, 10697, 67])).
% 1.96/2.13 tff(10701,plain,
% 1.96/2.13 (b(s(z), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[194, 10700])).
% 1.96/2.13 tff(10702,plain,
% 1.96/2.13 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8970, 10701, 28, 67, 7113, 10697, 293])).
% 1.96/2.13 tff(10703,plain,
% 1.96/2.13 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[105, 10702])).
% 1.96/2.13 tff(10704,plain,
% 1.96/2.13 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8492, 10697, 67, 228])).
% 1.96/2.13 tff(10705,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[226, 10704])).
% 1.96/2.13 tff(10706,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10707,plain,
% 1.96/2.13 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10708,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[10707])).
% 1.96/2.13 tff(10709,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[10708, 10706])).
% 1.96/2.13 tff(10710,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(10711,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10710, 10709])).
% 1.96/2.13 tff(10712,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10711, 116, 847, 10705, 10703, 28, 10699])).
% 1.96/2.13 tff(10713,plain,((~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | r(z, elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(10714,plain,
% 1.96/2.13 (~r(z, s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10713, 228, 28, 67, 847, 1052, 518])).
% 1.96/2.13 tff(10715,plain,
% 1.96/2.13 (b(z, s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[289, 10714])).
% 1.96/2.13 tff(10716,plain,
% 1.96/2.13 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3873, 1077, 847])).
% 1.96/2.13 tff(10717,plain,
% 1.96/2.13 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[1077])).
% 1.96/2.13 tff(10718,plain,
% 1.96/2.13 (b(z, s(s(s(s(z)))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[1055, 10717])).
% 1.96/2.13 tff(10719,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10720,plain,
% 1.96/2.13 (((~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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10721,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[10720])).
% 1.96/2.13 tff(10722,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[10721, 10719])).
% 1.96/2.13 tff(10723,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(10724,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[10723, 10722])).
% 1.96/2.13 tff(10725,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10724, 116, 271, 28, 1177, 10718, 10716])).
% 1.96/2.13 tff(10726,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(10727,plain,
% 1.96/2.13 (~(elem!1 = s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[10726, 10715, 28, 10695, 2040, 847])).
% 1.96/2.13 tff(10728,plain,
% 1.96/2.13 (r(elem!1, z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2115, 270, 847, 1052, 518])).
% 1.96/2.13 tff(10729,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1596, 8772, 2416])).
% 1.96/2.13 tff(10730,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10731,plain,
% 1.96/2.13 (((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(10732,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10731])).
% 1.96/2.14 tff(10733,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[10732, 10730])).
% 1.96/2.14 tff(10734,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(10735,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10734, 10733])).
% 1.96/2.14 tff(10736,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10735, 116, 1055, 847, 270, 3813, 10729])).
% 1.96/2.14 tff(10737,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10738,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10737, 10728, 270, 847, 2040, 228, 1362])).
% 1.96/2.14 tff(10739,plain,((~b(s(z), z)) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(s(z))))) | r(z, elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10740,plain,
% 1.96/2.14 (~b(s(z), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10739, 228, 847, 10727, 1052, 518])).
% 1.96/2.14 tff(10741,plain,
% 1.96/2.14 (r(s(z), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[210, 10740])).
% 1.96/2.14 tff(10742,plain,
% 1.96/2.14 (~r(s(z), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8864, 10741, 228])).
% 1.96/2.14 tff(10743,plain,
% 1.96/2.14 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[325, 10742])).
% 1.96/2.14 tff(10744,plain,
% 1.96/2.14 (~r(s(z), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7122, 10741, 67])).
% 1.96/2.14 tff(10745,plain,
% 1.96/2.14 (b(s(z), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[194, 10744])).
% 1.96/2.14 tff(10746,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8492, 10741, 67, 228])).
% 1.96/2.14 tff(10747,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[226, 10746])).
% 1.96/2.14 tff(10748,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10749,plain,
% 1.96/2.14 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10750,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10749])).
% 1.96/2.14 tff(10751,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[10750, 10748])).
% 1.96/2.14 tff(10752,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(z), s(s(s(s(z)))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(10753,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10752, 10751])).
% 1.96/2.14 tff(10754,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10753, 116, 10747, 28, 10695, 10745, 10743])).
% 1.96/2.14 tff(10755,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(z), elem!1)) | r(z, elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10756,plain,
% 1.96/2.14 (r(z, elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10755, 10687, 10674, 847, 10531, 10685])).
% 1.96/2.14 tff(10757,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8224, 77, 448, 428, 1212])).
% 1.96/2.14 tff(10758,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10759,plain,
% 1.96/2.14 (~r(s(s(z)), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10758, 10756, 1212])).
% 1.96/2.14 tff(10760,plain,
% 1.96/2.14 (b(s(s(z)), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[426, 10759, 10683])).
% 1.96/2.14 tff(10761,plain,
% 1.96/2.14 (~b(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7661, 10760, 10440, 10529])).
% 1.96/2.14 tff(10762,plain,
% 1.96/2.14 (r(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[545, 10761, 10675])).
% 1.96/2.14 tff(10763,plain,
% 1.96/2.14 (~r(elem!1, s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2671, 10762, 10531])).
% 1.96/2.14 tff(10764,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3287, 10756, 10531])).
% 1.96/2.14 tff(10765,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2549, 10531, 1212])).
% 1.96/2.14 tff(10766,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[226, 10765])).
% 1.96/2.14 tff(10767,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10768,plain,
% 1.96/2.14 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10769,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10768])).
% 1.96/2.14 tff(10770,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[10769, 10767])).
% 1.96/2.14 tff(10771,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(10772,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10771, 10770])).
% 1.96/2.14 tff(10773,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10772, 116, 212, 4412, 1331, 4413])).
% 1.96/2.14 tff(10774,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10775,plain,
% 1.96/2.14 (elem!1 = s(s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10774, 10766, 10760, 10764, 10763])).
% 1.96/2.14 tff(10776,plain,
% 1.96/2.14 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10775])).
% 1.96/2.14 tff(10777,plain,
% 1.96/2.14 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10776])).
% 1.96/2.14 tff(10778,plain,
% 1.96/2.14 (~r(s(s(s(z))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2717, 77, 10762, 10685])).
% 1.96/2.14 tff(10779,plain,
% 1.96/2.14 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10778, 10777])).
% 1.96/2.14 tff(10780,plain,
% 1.96/2.14 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1146, 10779])).
% 1.96/2.14 tff(10781,plain,
% 1.96/2.14 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10775])).
% 1.96/2.14 tff(10782,plain,
% 1.96/2.14 (b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10760, 10781])).
% 1.96/2.14 tff(10783,plain,
% 1.96/2.14 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7144, 10440, 7113, 292])).
% 1.96/2.14 tff(10784,plain,
% 1.96/2.14 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[105, 10783])).
% 1.96/2.14 tff(10785,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2471, 116, 10766, 7113, 10784, 10782, 10780])).
% 1.96/2.14 tff(10786,plain,((~r(z, s(s(z)))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10787,plain,
% 1.96/2.14 (~r(z, s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10786, 6090, 847, 3651])).
% 1.96/2.14 tff(10788,plain,
% 1.96/2.14 (b(z, s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1174, 10787])).
% 1.96/2.14 tff(10789,plain,
% 1.96/2.14 (~b(s(z), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7883, 116, 10529, 7113, 10788])).
% 1.96/2.14 tff(10790,plain,
% 1.96/2.14 (r(s(z), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[172, 10789])).
% 1.96/2.14 tff(10791,plain,
% 1.96/2.14 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2319, 10790, 6090])).
% 1.96/2.14 tff(10792,plain,
% 1.96/2.14 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[105, 10791])).
% 1.96/2.14 tff(10793,plain,
% 1.96/2.14 (~b(s(s(s(z))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8127, 10792, 7113, 10788])).
% 1.96/2.14 tff(10794,plain,
% 1.96/2.14 (r(s(s(s(z))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[63, 10793])).
% 1.96/2.14 tff(10795,plain,
% 1.96/2.14 (r(z, elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6099, 293, 847, 518, 270])).
% 1.96/2.14 tff(10796,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10797,plain,
% 1.96/2.14 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10798,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10797])).
% 1.96/2.14 tff(10799,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[10798, 10796])).
% 1.96/2.14 tff(10800,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(10801,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10800, 10799])).
% 1.96/2.14 tff(10802,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10801, 77, 448, 293, 67, 1047])).
% 1.96/2.14 tff(10803,plain,((~r(s(s(s(z))), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10804,plain,
% 1.96/2.14 (~r(s(s(s(z))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10803, 10795, 293, 67])).
% 1.96/2.14 tff(10805,plain,
% 1.96/2.14 (b(s(s(s(z))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[402, 21, 135, 10804])).
% 1.96/2.14 tff(10806,plain,
% 1.96/2.14 (~r(elem!1, s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[791, 293, 10795])).
% 1.96/2.14 tff(10807,plain,
% 1.96/2.14 (b(elem!1, s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[633, 10806, 3670])).
% 1.96/2.14 tff(10808,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10809,plain,
% 1.96/2.14 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10810,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10809])).
% 1.96/2.14 tff(10811,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[10810, 10808])).
% 1.96/2.14 tff(10812,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(10813,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10812, 10811])).
% 1.96/2.14 tff(10814,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10813, 116, 537, 270, 667, 7113, 2442])).
% 1.96/2.14 tff(10815,plain,((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10816,plain,
% 1.96/2.14 (~b(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10815, 10807, 270, 2442])).
% 1.96/2.14 tff(10817,plain,
% 1.96/2.14 (r(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[545, 10816, 534])).
% 1.96/2.14 tff(10818,plain,
% 1.96/2.14 (~r(elem!1, s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2162, 77, 10817, 67])).
% 1.96/2.14 tff(10819,plain,
% 1.96/2.14 (b(elem!1, s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1345, 10818, 1620])).
% 1.96/2.14 tff(10820,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10821,plain,
% 1.96/2.14 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10822,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10821])).
% 1.96/2.14 tff(10823,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[10822, 10820])).
% 1.96/2.14 tff(10824,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(10825,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10824, 10823])).
% 1.96/2.14 tff(10826,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10825, 116, 847, 10807, 10819, 10805])).
% 1.96/2.14 tff(10827,plain,((~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(10828,plain,
% 1.96/2.14 (~r(z, s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10827, 10794, 847, 6121, 10529, 10788, 10674])).
% 1.96/2.14 tff(10829,plain,
% 1.96/2.14 (b(z, s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[289, 10828])).
% 1.96/2.14 tff(10830,plain,
% 1.96/2.14 (~b(s(s(s(s(z)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10163, 10829, 10529])).
% 1.96/2.14 tff(10831,plain,
% 1.96/2.14 (r(s(s(s(s(z)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[247, 10830])).
% 1.96/2.14 tff(10832,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3961, 10831, 10794])).
% 1.96/2.14 tff(10833,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3951, 10832])).
% 1.96/2.14 tff(10834,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(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))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10835,plain,
% 1.96/2.14 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(10836,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[10835])).
% 1.96/2.14 tff(10837,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[10836, 10834])).
% 1.96/2.14 tff(10838,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(10839,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10838, 10837])).
% 1.96/2.14 tff(10840,plain,
% 1.96/2.14 (~r(s(s(s(s(s(z))))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[10839, 77, 292, 1904])).
% 1.96/2.15 tff(10841,plain,
% 1.96/2.15 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[5816, 21, 10840])).
% 1.96/2.15 tff(10842,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10841, 5783])).
% 1.96/2.15 tff(10843,plain,
% 1.96/2.15 (~b(s(s(s(s(s(z))))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6679, 116, 270, 271, 10842])).
% 1.96/2.15 tff(10844,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[898, 21, 895, 10843])).
% 1.96/2.15 tff(10845,plain,
% 1.96/2.15 (~b(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10652, 271, 270])).
% 1.96/2.15 tff(10846,plain,
% 1.96/2.15 (r(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[63, 10845])).
% 1.96/2.15 tff(10847,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10848,plain,
% 1.96/2.15 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10849,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[10848])).
% 1.96/2.15 tff(10850,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[10849, 10847])).
% 1.96/2.15 tff(10851,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(10852,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10851, 10850])).
% 1.96/2.15 tff(10853,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10852, 77, 10846, 1904, 10844])).
% 1.96/2.15 tff(10854,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(10855,plain,
% 1.96/2.15 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10854, 10829, 10529, 6090])).
% 1.96/2.15 tff(10856,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1380, 10855])).
% 1.96/2.15 tff(10857,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10858,plain,
% 1.96/2.15 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10859,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[10858])).
% 1.96/2.15 tff(10860,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[10859, 10857])).
% 1.96/2.15 tff(10861,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(10862,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10861, 10860])).
% 1.96/2.15 tff(10863,plain,
% 1.96/2.15 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10862, 116, 27, 28, 1177, 5031])).
% 1.96/2.15 tff(10864,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 10863])).
% 1.96/2.15 tff(10865,plain,
% 1.96/2.15 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10578, 116, 28, 1177, 5031])).
% 1.96/2.15 tff(10866,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6694, 10865])).
% 1.96/2.15 tff(10867,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10211, 77, 328, 10866, 10864])).
% 1.96/2.15 tff(10868,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(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(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(10869,plain,
% 1.96/2.15 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10868, 328, 28, 5031, 27])).
% 1.96/2.15 tff(10870,plain,
% 1.96/2.15 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1146, 10869])).
% 1.96/2.15 tff(10871,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10872,plain,
% 1.96/2.15 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10873,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[10872])).
% 1.96/2.15 tff(10874,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[10873, 10871])).
% 1.96/2.15 tff(10875,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(10876,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10875, 10874])).
% 1.96/2.15 tff(10877,plain,
% 1.96/2.15 (~r(s(s(s(z))), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10876, 77, 328, 10870])).
% 1.96/2.15 tff(10878,plain,
% 1.96/2.15 (b(s(s(s(z))), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[89, 21, 10877, 56])).
% 1.96/2.15 tff(10879,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10880,plain,
% 1.96/2.15 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10881,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[10880])).
% 1.96/2.15 tff(10882,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[10881, 10879])).
% 1.96/2.15 tff(10883,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(10884,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10883, 10882])).
% 1.96/2.15 tff(10885,plain,
% 1.96/2.15 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10884, 116, 7113, 27, 10878, 5031])).
% 1.96/2.15 tff(10886,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 10885])).
% 1.96/2.15 tff(10887,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10888,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(10889,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10888, 10887])).
% 1.96/2.15 tff(10890,plain,
% 1.96/2.15 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10889, 116, 7113, 28, 10878, 5031])).
% 1.96/2.15 tff(10891,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6694, 10890])).
% 1.96/2.15 tff(10892,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10211, 77, 328, 10891, 10886])).
% 1.96/2.15 tff(10893,plain,((~r(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(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(10894,plain,
% 1.96/2.15 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10893, 10833, 10856, 10792])).
% 1.96/2.15 tff(10895,plain,
% 1.96/2.15 (b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[149, 10894])).
% 1.96/2.15 tff(10896,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10897,plain,
% 1.96/2.15 (((~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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10898,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[10897])).
% 1.96/2.15 tff(10899,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[10898, 10896])).
% 1.96/2.15 tff(10900,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(10901,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10900, 10899])).
% 1.96/2.15 tff(10902,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10901, 116, 27, 2410, 28, 1177])).
% 1.96/2.15 tff(10903,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(10904,plain,
% 1.96/2.15 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10903, 10792, 10895, 10833])).
% 1.96/2.15 tff(10905,plain,
% 1.96/2.15 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1146, 10904])).
% 1.96/2.15 tff(10906,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10693, 77, 10794, 10831, 10905])).
% 1.96/2.15 tff(10907,plain,(b(s(z), s(s(s(z)))) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(10908,plain,
% 1.96/2.15 (b(s(z), s(s(s(z))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10907, 847, 3651])).
% 1.96/2.15 tff(10909,plain,
% 1.96/2.15 (~b(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3291, 10440, 10529, 10908])).
% 1.96/2.15 tff(10910,plain,
% 1.96/2.15 (r(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[63, 10909])).
% 1.96/2.15 tff(10911,plain,
% 1.96/2.15 (~b(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10163, 271, 270])).
% 1.96/2.15 tff(10912,plain,
% 1.96/2.15 (r(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[247, 10911])).
% 1.96/2.15 tff(10913,plain,
% 1.96/2.15 (~b(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3291, 271, 270, 175])).
% 1.96/2.15 tff(10914,plain,
% 1.96/2.15 (r(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[63, 10913])).
% 1.96/2.15 tff(10915,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3961, 10914, 10912, 3953])).
% 1.96/2.15 tff(10916,plain,((~b(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(10917,plain,
% 1.96/2.15 (~b(z, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10916, 3953, 10529, 10908])).
% 1.96/2.15 tff(10918,plain,
% 1.96/2.15 (r(z, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[289, 10917])).
% 1.96/2.15 tff(10919,plain,
% 1.96/2.15 (~r(z, s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10422, 10918, 3651])).
% 1.96/2.15 tff(10920,plain,
% 1.96/2.15 (b(z, s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1174, 10919])).
% 1.96/2.15 tff(10921,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10922,plain,
% 1.96/2.15 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(10923,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[10922])).
% 1.96/2.15 tff(10924,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.96/2.15 inference(transitivity,[status(thm)],[10923, 10921])).
% 1.96/2.15 tff(10925,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(10926,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10925, 10924])).
% 1.96/2.15 tff(10927,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10926, 116, 270, 2247, 7113, 2442, 175])).
% 1.96/2.15 tff(10928,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(10929,plain,
% 1.96/2.15 (~b(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10928, 10920, 10529, 10908])).
% 1.96/2.15 tff(10930,plain,
% 1.96/2.15 (r(s(s(s(z))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[63, 10929])).
% 1.96/2.15 tff(10931,plain,
% 1.96/2.15 (~r(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3961, 10930, 3953])).
% 1.96/2.15 tff(10932,plain,
% 1.96/2.15 (b(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[247, 10931])).
% 1.96/2.15 tff(10933,plain,
% 1.96/2.15 (elem!1 = s(s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10827, 10930, 847, 10918, 10529, 10920, 10674])).
% 1.96/2.15 tff(10934,plain,
% 1.96/2.15 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[10933])).
% 1.96/2.15 tff(10935,plain,
% 1.96/2.15 (r(z, elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6099, 10918, 847, 10674, 10529])).
% 1.96/2.15 tff(10936,plain,
% 1.96/2.15 (~r(elem!1, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[791, 10918, 10935])).
% 1.96/2.15 tff(10937,plain,
% 1.96/2.15 (b(elem!1, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[633, 10936, 3670])).
% 1.96/2.15 tff(10938,plain,
% 1.96/2.15 (b(s(s(s(z))), s(z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[10937, 10934])).
% 1.96/2.15 tff(10939,plain,
% 1.96/2.15 (~b(s(s(z)), s(s(s(z))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[10396, 10938, 10908, 10920, 10932, 847])).
% 1.96/2.16 tff(10940,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[105, 10939])).
% 1.96/2.16 tff(10941,plain,
% 1.96/2.16 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4984, 77, 10940, 3953])).
% 1.96/2.16 tff(10942,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[226, 10941])).
% 1.96/2.16 tff(10943,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10358, 116, 10942, 7113, 10920, 10932])).
% 1.96/2.16 tff(10944,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(10945,plain,
% 1.96/2.16 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10944, 847, 3651])).
% 1.96/2.16 tff(10946,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3951, 10945])).
% 1.96/2.16 tff(10947,plain,
% 1.96/2.16 (r(z, elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10755, 10531, 10674, 847, 10946, 10910])).
% 1.96/2.16 tff(10948,plain,
% 1.96/2.16 (~r(s(s(z)), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10758, 10947, 1212])).
% 1.96/2.16 tff(10949,plain,
% 1.96/2.16 (b(s(s(z)), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[426, 10683, 10948])).
% 1.96/2.16 tff(10950,plain,
% 1.96/2.16 (~r(s(s(s(s(z)))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3287, 10947, 10531])).
% 1.96/2.16 tff(10951,plain,
% 1.96/2.16 (~b(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7661, 10949, 10440, 10529])).
% 1.96/2.16 tff(10952,plain,
% 1.96/2.16 (r(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[545, 10951, 10675])).
% 1.96/2.16 tff(10953,plain,
% 1.96/2.16 (~r(elem!1, s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2671, 10952, 10531])).
% 1.96/2.16 tff(10954,plain,
% 1.96/2.16 (elem!1 = s(s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10774, 10953, 10950, 10766, 10949])).
% 1.96/2.16 tff(10955,plain,
% 1.96/2.16 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3873, 10954, 847])).
% 1.96/2.16 tff(10956,plain,
% 1.96/2.16 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10693, 77, 10910, 10531])).
% 1.96/2.16 tff(10957,plain,
% 1.96/2.16 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1146, 10956])).
% 1.96/2.16 tff(10958,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(10959,plain,
% 1.96/2.16 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(10960,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10959])).
% 1.96/2.16 tff(10961,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[10960, 10958])).
% 1.96/2.16 tff(10962,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(10963,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[10962, 10961])).
% 1.96/2.16 tff(10964,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10963, 116, 10766, 7113, 10957, 10908, 10955])).
% 1.96/2.16 tff(10965,plain,((~r(z, s(s(z)))) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(10966,plain,
% 1.96/2.16 (~r(z, s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10965, 10250, 7120])).
% 1.96/2.16 tff(10967,plain,
% 1.96/2.16 (b(z, s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1174, 10966])).
% 1.96/2.16 tff(10968,plain,
% 1.96/2.16 (~r(s(z), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10527, 7120, 10250])).
% 1.96/2.16 tff(10969,plain,
% 1.96/2.16 (b(s(z), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[210, 10968])).
% 1.96/2.16 tff(10970,plain,
% 1.96/2.16 (~b(s(z), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7883, 116, 10969, 7113, 10967])).
% 1.96/2.16 tff(10971,plain,
% 1.96/2.16 (~(s(s(z)) = elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2038, 10970, 10250])).
% 1.96/2.16 tff(10972,plain,
% 1.96/2.16 (~(z = elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10673, 10250, 7120])).
% 1.96/2.16 tff(10973,plain,
% 1.96/2.16 (b(s(z), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10907, 10250, 7120])).
% 1.96/2.16 tff(10974,plain,
% 1.96/2.16 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10944, 10250, 7120])).
% 1.96/2.16 tff(10975,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3951, 10974])).
% 1.96/2.16 tff(10976,plain,
% 1.96/2.16 (~b(s(s(s(z))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10928, 2442, 270, 175])).
% 1.96/2.16 tff(10977,plain,
% 1.96/2.16 (r(s(s(s(z))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[63, 10976])).
% 1.96/2.16 tff(10978,plain,
% 1.96/2.16 (elem!1 = s(s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10827, 293, 847, 10977, 270, 2442, 518])).
% 1.96/2.16 tff(10979,plain,
% 1.96/2.16 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10978])).
% 1.96/2.16 tff(10980,plain,
% 1.96/2.16 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10978])).
% 1.96/2.16 tff(10981,plain,
% 1.96/2.16 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.16 inference(symmetry,[status(thm)],[10980])).
% 1.96/2.16 tff(10982,plain,
% 1.96/2.16 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10981])).
% 1.96/2.16 tff(10983,plain,
% 1.96/2.16 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[1138, 10982])).
% 1.96/2.16 tff(10984,plain,
% 1.96/2.16 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10978])).
% 1.96/2.16 tff(10985,plain,
% 1.96/2.16 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.96/2.16 inference(symmetry,[status(thm)],[10984])).
% 1.96/2.16 tff(10986,plain,
% 1.96/2.16 (s(elem!1) = s(s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10978])).
% 1.96/2.16 tff(10987,plain,
% 1.96/2.16 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10986])).
% 1.96/2.16 tff(10988,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[10987])).
% 1.96/2.16 tff(10989,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.96/2.16 inference(transitivity,[status(thm)],[10988, 10985])).
% 1.96/2.16 tff(10990,plain,
% 1.96/2.16 (b(s(elem!1), elem!1)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[28, 10989])).
% 1.96/2.16 tff(10991,plain,
% 1.96/2.16 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10986])).
% 1.96/2.16 tff(10992,plain,
% 1.96/2.16 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[10991, 1393])).
% 1.96/2.16 tff(10993,plain,
% 1.96/2.16 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[10992])).
% 1.96/2.16 tff(10994,plain,
% 1.96/2.16 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10993])).
% 1.96/2.16 tff(10995,plain,
% 1.96/2.16 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[6647, 10994])).
% 1.96/2.16 tff(10996,plain,
% 1.96/2.16 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10986])).
% 1.96/2.16 tff(10997,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.96/2.16 inference(symmetry,[status(thm)],[10996])).
% 1.96/2.16 tff(10998,plain,
% 1.96/2.16 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[10978])).
% 1.96/2.16 tff(10999,plain,
% 1.96/2.16 (b(s(s(s(z))), s(z))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[10807, 10998])).
% 1.96/2.16 tff(11000,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11001,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(11002,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11001, 11000])).
% 1.96/2.16 tff(11003,plain,
% 1.96/2.16 (~b(s(s(s(s(z)))), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11002, 116, 270, 28, 175, 10999])).
% 1.96/2.16 tff(11004,plain,
% 1.96/2.16 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2054, 21, 11003])).
% 1.96/2.16 tff(11005,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11004, 2044])).
% 1.96/2.16 tff(11006,plain,
% 1.96/2.16 (r(s(elem!1), s(z))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11005, 10997])).
% 1.96/2.16 tff(11007,plain,
% 1.96/2.16 ((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[880, 1901])).
% 1.96/2.16 tff(11008,plain,
% 1.96/2.16 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11007, 11006, 847, 10995, 10990, 10807])).
% 1.96/2.16 tff(11009,plain,
% 1.96/2.16 (r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[885, 11008, 10983])).
% 1.96/2.16 tff(11010,plain,
% 1.96/2.16 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11009, 10979])).
% 1.96/2.16 tff(11011,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11012,plain,
% 1.96/2.16 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11013,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11012])).
% 1.96/2.16 tff(11014,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[11013, 11011])).
% 1.96/2.16 tff(11015,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(11016,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11015, 11014])).
% 1.96/2.16 tff(11017,plain,
% 1.96/2.16 (~r(s(s(s(s(z)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11016, 77, 293, 11005])).
% 1.96/2.16 tff(11018,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[247, 11017])).
% 1.96/2.16 tff(11019,plain,
% 1.96/2.16 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[6419, 11018, 270, 10795, 10978, 10995])).
% 1.96/2.16 tff(11020,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11019, 11010])).
% 1.96/2.16 tff(11021,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(11022,plain,
% 1.96/2.16 (~r(z, s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11021, 10969, 10250, 10975, 10973, 10967, 10972])).
% 1.96/2.16 tff(11023,plain,
% 1.96/2.16 (b(z, s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[289, 11022])).
% 1.96/2.16 tff(11024,plain,
% 1.96/2.16 (~b(s(s(s(s(z)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10163, 11023, 10969])).
% 1.96/2.16 tff(11025,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[247, 11024])).
% 1.96/2.16 tff(11026,plain,
% 1.96/2.16 (~b(s(s(s(z))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10928, 10967, 10969, 10973])).
% 1.96/2.16 tff(11027,plain,
% 1.96/2.16 (r(s(s(s(z))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[63, 11026])).
% 1.96/2.16 tff(11028,plain,
% 1.96/2.16 (((~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(z), s(s(s(s(z)))))) | (~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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11029,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(s(s(s(z))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11028])).
% 1.96/2.16 tff(11030,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[11029, 8485])).
% 1.96/2.16 tff(11031,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(11032,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11031, 11030])).
% 1.96/2.16 tff(11033,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11032, 116, 28, 10695, 175, 249])).
% 1.96/2.16 tff(11034,plain,((~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))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(11035,plain,
% 1.96/2.16 (~b(s(z), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11034, 10975, 10973, 11027, 11025])).
% 1.96/2.16 tff(11036,plain,
% 1.96/2.16 (~(elem!1 = s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3873, 11035, 10250])).
% 1.96/2.16 tff(11037,plain,
% 1.96/2.16 (r(z, elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10755, 11025, 10972, 10250, 10975, 11027])).
% 1.96/2.16 tff(11038,plain,
% 1.96/2.16 (~r(s(s(s(s(z)))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3287, 11025, 11037])).
% 1.96/2.16 tff(11039,plain,
% 1.96/2.16 (~(elem!1 = z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[533, 10972])).
% 1.96/2.16 tff(11040,plain,
% 1.96/2.16 (r(s(z), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[172, 10970])).
% 1.96/2.16 tff(11041,plain,
% 1.96/2.16 (r(s(z), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[325, 11035])).
% 1.96/2.16 tff(11042,plain,
% 1.96/2.16 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[336, 11041, 11040])).
% 1.96/2.16 tff(11043,plain,
% 1.96/2.16 (b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[149, 11042])).
% 1.96/2.16 tff(11044,plain,
% 1.96/2.16 (r(elem!1, s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4415, 1331, 2410, 1362, 3289])).
% 1.96/2.16 tff(11045,plain,
% 1.96/2.16 (~b(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7661, 1331, 271, 270])).
% 1.96/2.16 tff(11046,plain,
% 1.96/2.16 (r(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[545, 11045, 439])).
% 1.96/2.16 tff(11047,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2671, 11046, 11044, 10912])).
% 1.96/2.16 tff(11048,plain,((~b(s(s(z)), elem!1)) | (elem!1 = z) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(11049,plain,
% 1.96/2.16 (~b(s(s(z)), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11048, 11043, 11023, 11039, 11038, 11036, 10969])).
% 1.96/2.16 tff(11050,plain,
% 1.96/2.16 (r(s(s(z)), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[426, 11049, 10971])).
% 1.96/2.16 tff(11051,plain,
% 1.96/2.16 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10693, 77, 11027, 11025])).
% 1.96/2.16 tff(11052,plain,
% 1.96/2.16 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1146, 11051])).
% 1.96/2.16 tff(11053,plain,
% 1.96/2.16 (~b(s(s(z)), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[10903, 11052, 11043, 10975])).
% 1.96/2.16 tff(11054,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[105, 11053])).
% 1.96/2.16 tff(11055,plain,
% 1.96/2.16 (~r(elem!1, s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[5025, 11054, 11050])).
% 1.96/2.16 tff(11056,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11057,plain,
% 1.96/2.16 (((~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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11058,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11057])).
% 1.96/2.16 tff(11059,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[11058, 11056])).
% 1.96/2.16 tff(11060,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(11061,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11060, 11059])).
% 1.96/2.16 tff(11062,plain,
% 1.96/2.16 (~b(s(s(s(z))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11061, 116, 11043, 10975, 11052])).
% 1.96/2.16 tff(11063,plain,
% 1.96/2.16 (r(s(s(s(z))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[89, 21, 11062, 56])).
% 1.96/2.16 tff(11064,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11065,plain,
% 1.96/2.16 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11066,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11065])).
% 1.96/2.16 tff(11067,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[11066, 11064])).
% 1.96/2.16 tff(11068,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(11069,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11068, 11067])).
% 1.96/2.16 tff(11070,plain,
% 1.96/2.16 (~r(s(s(s(z))), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[11069, 77, 11063, 11040])).
% 1.96/2.16 tff(11071,plain,
% 1.96/2.16 (b(s(s(s(z))), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[402, 21, 135, 11070])).
% 1.96/2.16 tff(11072,plain,
% 1.96/2.16 (~b(elem!1, s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8639, 11071, 10250, 10973])).
% 1.96/2.16 tff(11073,plain,
% 1.96/2.16 (elem!1 = s(s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1345, 11072, 11055])).
% 1.96/2.16 tff(11074,plain,
% 1.96/2.16 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11073])).
% 1.96/2.16 tff(11075,plain,
% 1.96/2.16 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11073])).
% 1.96/2.16 tff(11076,plain,
% 1.96/2.16 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.16 inference(symmetry,[status(thm)],[11075])).
% 1.96/2.16 tff(11077,plain,
% 1.96/2.16 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11076])).
% 1.96/2.16 tff(11078,plain,
% 1.96/2.16 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[1138, 11077])).
% 1.96/2.16 tff(11079,plain,
% 1.96/2.16 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11073])).
% 1.96/2.16 tff(11080,plain,
% 1.96/2.16 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.96/2.16 inference(symmetry,[status(thm)],[11079])).
% 1.96/2.16 tff(11081,plain,
% 1.96/2.16 (b(elem!1, s(z))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[11071, 11080])).
% 1.96/2.16 tff(11082,plain,
% 1.96/2.16 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11073])).
% 1.96/2.16 tff(11083,plain,
% 1.96/2.16 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.96/2.16 inference(symmetry,[status(thm)],[11082])).
% 1.96/2.16 tff(11084,plain,
% 1.96/2.16 (s(elem!1) = s(s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11073])).
% 1.96/2.16 tff(11085,plain,
% 1.96/2.16 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11084])).
% 1.96/2.16 tff(11086,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[11085])).
% 1.96/2.16 tff(11087,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.96/2.16 inference(transitivity,[status(thm)],[11086, 11083])).
% 1.96/2.16 tff(11088,plain,
% 1.96/2.16 (b(s(elem!1), elem!1)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[10975, 11087])).
% 1.96/2.16 tff(11089,plain,
% 1.96/2.16 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1364, 11036])).
% 1.96/2.16 tff(11090,plain,
% 1.96/2.16 (r(s(elem!1), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[11084])).
% 1.96/2.16 tff(11091,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.96/2.16 inference(symmetry,[status(thm)],[11090])).
% 1.96/2.16 tff(11092,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(11093,plain,
% 1.96/2.16 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11094,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11093])).
% 1.96/2.17 tff(11095,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[11094, 11092])).
% 1.96/2.17 tff(11096,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(11097,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11096, 11095])).
% 1.96/2.17 tff(11098,plain,
% 1.96/2.17 (~b(s(s(s(s(z)))), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11097, 116, 10975, 11052, 10973])).
% 1.96/2.17 tff(11099,plain,
% 1.96/2.17 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2054, 21, 11098])).
% 1.96/2.17 tff(11100,plain,
% 1.96/2.17 (r(s(s(s(s(z)))), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11099, 2044])).
% 1.96/2.17 tff(11101,plain,
% 1.96/2.17 (r(s(elem!1), s(z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11100, 11091])).
% 1.96/2.17 tff(11102,plain,
% 1.96/2.17 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11007, 11101, 10250, 11089, 11088, 11081])).
% 1.96/2.17 tff(11103,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[885, 11102, 11078])).
% 1.96/2.17 tff(11104,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11103, 11074])).
% 1.96/2.17 tff(11105,plain,
% 1.96/2.17 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4997, 77, 11054, 11104])).
% 1.96/2.17 tff(11106,plain,
% 1.96/2.17 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1391, 21, 1202, 11105])).
% 1.96/2.17 tff(11107,plain,
% 1.96/2.17 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11073])).
% 1.96/2.17 tff(11108,plain,
% 1.96/2.17 (r(z, s(s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11037, 11107])).
% 1.96/2.17 tff(11109,plain,
% 1.96/2.17 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[10378, 77, 11104, 11108])).
% 1.96/2.17 tff(11110,plain,
% 1.96/2.17 (b(s(s(s(s(s(z))))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[898, 21, 895, 11109])).
% 1.96/2.17 tff(11111,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[10498, 116, 11023, 7113, 10967, 11110, 11106])).
% 1.96/2.17 tff(11112,plain,(b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11113,plain,
% 1.96/2.17 (~r(s(z), s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[3975, 3953, 292])).
% 1.96/2.17 tff(11114,plain,
% 1.96/2.17 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[325, 11113])).
% 1.96/2.17 tff(11115,plain,
% 1.96/2.17 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6779, 116, 11112, 11114, 6558])).
% 1.96/2.17 tff(11116,plain,
% 1.96/2.17 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[226, 11115])).
% 1.96/2.17 tff(11117,plain,
% 1.96/2.17 (~r(s(z), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2319, 2235, 292])).
% 1.96/2.17 tff(11118,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11119,plain,
% 1.96/2.17 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11120,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11119])).
% 1.96/2.17 tff(11121,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[11120, 11118])).
% 1.96/2.17 tff(11122,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(11123,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11122, 11121])).
% 1.96/2.17 tff(11124,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11123, 116, 4986, 1303, 5008, 174, 249])).
% 1.96/2.17 tff(11125,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11126,plain,
% 1.96/2.17 ((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11125, 7113])).
% 1.96/2.17 tff(11127,plain,
% 1.96/2.17 (~b(s(z), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11126, 2235, 11114, 3953])).
% 1.96/2.17 tff(11128,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[172, 11127, 11117])).
% 1.96/2.17 tff(11129,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11130,plain,
% 1.96/2.17 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11129, 3953, 292])).
% 1.96/2.17 tff(11131,plain,
% 1.96/2.17 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[105, 11130])).
% 1.96/2.17 tff(11132,plain,
% 1.96/2.17 ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8127, 7113])).
% 1.96/2.17 tff(11133,plain,
% 1.96/2.17 (~b(z, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11132, 11131, 2247])).
% 1.96/2.17 tff(11134,plain,
% 1.96/2.17 (r(z, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1174, 11133])).
% 1.96/2.17 tff(11135,plain,
% 1.96/2.17 (~r(z, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1572, 11134, 11116])).
% 1.96/2.17 tff(11136,plain,
% 1.96/2.17 (b(z, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1576, 21, 11135, 1563])).
% 1.96/2.17 tff(11137,plain,
% 1.96/2.17 (~r(s(s(s(s(z)))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2549, 11134, 11116])).
% 1.96/2.17 tff(11138,plain,
% 1.96/2.17 (b(s(s(s(s(z)))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[247, 11137])).
% 1.96/2.17 tff(11139,plain,
% 1.96/2.17 (~r(z, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1572, 1212, 229])).
% 1.96/2.17 tff(11140,plain,
% 1.96/2.17 (b(z, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1576, 21, 11139, 1563])).
% 1.96/2.17 tff(11141,plain,
% 1.96/2.17 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11126, 10274, 249, 3953])).
% 1.96/2.17 tff(11142,plain,
% 1.96/2.17 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[105, 11141])).
% 1.96/2.17 tff(11143,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11144,plain,
% 1.96/2.17 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11145,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11144])).
% 1.96/2.17 tff(11146,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.96/2.17 inference(transitivity,[status(thm)],[11145, 11143])).
% 1.96/2.17 tff(11147,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(11148,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11147, 11146])).
% 1.96/2.17 tff(11149,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11148, 116, 2247, 7113, 11142, 254, 11140])).
% 1.96/2.17 tff(11150,plain,((~r(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11151,plain,
% 1.96/2.17 (~r(s(z), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11150, 11138, 2247, 11114, 3953, 11134, 11116])).
% 1.96/2.17 tff(11152,plain,
% 1.96/2.17 (b(s(z), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[210, 11151])).
% 1.96/2.17 tff(11153,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11154,plain,
% 1.96/2.17 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11155,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11154])).
% 1.96/2.17 tff(11156,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[11155, 11153])).
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% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
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% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11157, 11156])).
% 1.96/2.17 tff(11159,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11158, 116, 11152, 11138, 11136, 6558])).
% 1.96/2.17 tff(11160,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11161,plain,
% 1.96/2.17 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11160, 2247, 6090])).
% 1.96/2.17 tff(11162,plain,
% 1.96/2.17 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[3951, 11161])).
% 1.96/2.17 tff(11163,plain,
% 1.96/2.17 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.96/2.17 inference(commutativity,[status(thm)],[])).
% 1.96/2.17 tff(11164,plain,
% 1.96/2.17 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2549, 1212, 228])).
% 1.96/2.17 tff(11165,plain,
% 1.96/2.17 (b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[226, 11164])).
% 1.96/2.17 tff(11166,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2272, 116, 11165, 11112, 10274, 10256])).
% 1.96/2.17 tff(11167,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11168,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[11167, 228, 3406])).
% 1.96/2.17 tff(11169,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[1174, 11168])).
% 1.96/2.17 tff(11170,plain,
% 1.96/2.17 (~b(s(s(z)), s(s(s(z))))),
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% 1.96/2.17 tff(11171,plain,
% 1.96/2.17 (r(s(s(z)), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[105, 11170])).
% 1.96/2.17 tff(11172,plain,
% 1.96/2.17 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11160, 2247, 292])).
% 1.96/2.17 tff(11173,plain,
% 1.96/2.17 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[3951, 11172])).
% 1.96/2.17 tff(11174,plain,
% 1.96/2.17 (~(z = elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[10042, 340, 11173, 2247, 11171])).
% 1.96/2.17 tff(11175,plain,
% 1.96/2.17 ((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7144, 7113])).
% 1.96/2.17 tff(11176,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[11175, 11171, 292])).
% 1.96/2.17 tff(11177,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[4796, 5634, 4794])).
% 1.96/2.17 tff(11178,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[357, 11177, 340])).
% 1.96/2.17 tff(11179,plain,
% 1.96/2.17 (~b(s(s(z)), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8268, 11177, 2247, 340, 5634, 534])).
% 1.96/2.17 tff(11180,plain,
% 1.96/2.17 (~(elem!1 = s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4700, 340, 10256])).
% 1.96/2.17 tff(11181,plain,
% 1.96/2.17 (r(elem!1, z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8572, 11178, 340, 155, 11180, 11179, 228, 1052])).
% 1.96/2.17 tff(11182,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[2815, 11181, 11178, 155])).
% 1.96/2.17 tff(11183,plain,(r(z, elem!1) | (~r(s(z), z)) | b(s(z), elem!1) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | b(z, s(z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11184,plain,
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% 1.96/2.17 (s(z) = elem!1),
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% 1.96/2.17 tff(11187,plain,
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% 1.96/2.17 tff(11189,plain,
% 1.96/2.17 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11188])).
% 1.96/2.17 tff(11190,plain,
% 1.96/2.17 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[11189])).
% 1.96/2.17 tff(11191,plain,
% 1.96/2.17 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11188])).
% 1.96/2.17 tff(11192,plain,
% 1.96/2.17 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
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% 1.96/2.17 tff(11193,plain,
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% 1.96/2.17 tff(11194,plain,
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% 1.96/2.17 tff(11195,plain,
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% 1.96/2.17 tff(11197,plain,
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% 1.96/2.17 tff(11199,plain,
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% 1.96/2.17 tff(11200,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[4700, 340, 11199])).
% 1.96/2.17 tff(11201,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[1984, 11186])).
% 1.96/2.17 tff(11203,plain,
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[1992, 11202, 1989])).
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% 1.96/2.17 inference(unit_resolution,[status(thm)],[545, 11203, 11201])).
% 1.96/2.17 tff(11205,plain,
% 1.96/2.17 (~r(elem!1, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2671, 11204, 228])).
% 1.96/2.17 tff(11206,plain,
% 1.96/2.17 (b(elem!1, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1068, 11205, 11200])).
% 1.96/2.17 tff(11207,plain,
% 1.96/2.17 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11186])).
% 1.96/2.17 tff(11208,plain,
% 1.96/2.17 (r(elem!1, s(s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[292, 11207])).
% 1.96/2.17 tff(11209,plain,
% 1.96/2.17 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11188])).
% 1.96/2.17 tff(11210,plain,
% 1.96/2.17 (r(elem!1, s(s(elem!1)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11208, 11209])).
% 1.96/2.17 tff(11211,plain,
% 1.96/2.17 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11186])).
% 1.96/2.17 tff(11212,plain,
% 1.96/2.17 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.17 inference(transitivity,[status(thm)],[11211, 4222])).
% 1.96/2.17 tff(11213,plain,
% 1.96/2.17 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11212])).
% 1.96/2.17 tff(11214,plain,
% 1.96/2.17 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[1901, 11213])).
% 1.96/2.17 tff(11215,plain,
% 1.96/2.17 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1364, 11200])).
% 1.96/2.17 tff(11216,plain,
% 1.96/2.17 (b(s(s(z)), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8169, 11186, 292, 2247, 1989, 340, 11174])).
% 1.96/2.17 tff(11217,plain,
% 1.96/2.17 (b(s(elem!1), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1549, 11186, 11216])).
% 1.96/2.17 tff(11218,plain,
% 1.96/2.17 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11187])).
% 1.96/2.17 tff(11219,plain,
% 1.96/2.17 (r(s(elem!1), s(s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11171, 11218])).
% 1.96/2.17 tff(11220,plain,
% 1.96/2.17 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1928, 11219, 11217, 11215, 11173, 11214, 11210, 11208, 11206])).
% 1.96/2.17 tff(11221,plain,
% 1.96/2.17 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1380, 11220])).
% 1.96/2.17 tff(11222,plain,
% 1.96/2.17 (~b(z, s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9959, 11221, 2247, 11173, 11193])).
% 1.96/2.17 tff(11223,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11222, 11197])).
% 1.96/2.17 tff(11224,plain,(b(s(z), elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11225,plain,
% 1.96/2.17 (b(s(z), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11224, 228, 6090, 2247, 1989])).
% 1.96/2.17 tff(11226,plain,
% 1.96/2.17 (~(elem!1 = z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6442, 11225, 1989])).
% 1.96/2.17 tff(11227,plain,
% 1.96/2.17 (~(z = elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[445, 11226])).
% 1.96/2.17 tff(11228,plain,
% 1.96/2.17 (~(elem!1 = s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1667, 11225, 1664])).
% 1.96/2.17 tff(11229,plain,
% 1.96/2.17 (~r(z, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11167, 228, 155])).
% 1.96/2.17 tff(11230,plain,
% 1.96/2.17 (b(z, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1174, 11229])).
% 1.96/2.17 tff(11231,plain,
% 1.96/2.17 (~b(s(s(z)), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11132, 11230, 2247])).
% 1.96/2.17 tff(11232,plain,
% 1.96/2.17 (r(s(s(z)), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[105, 11231])).
% 1.96/2.17 tff(11233,plain,
% 1.96/2.17 ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(s(z), z)) | (elem!1 = s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6457, 11112])).
% 1.96/2.17 tff(11234,plain,
% 1.96/2.17 (~b(s(s(z)), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11233, 1055, 155, 847, 439, 3670])).
% 1.96/2.17 tff(11235,plain,
% 1.96/2.17 (~r(elem!1, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2671, 6483, 228])).
% 1.96/2.17 tff(11236,plain,
% 1.96/2.17 (b(elem!1, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1068, 11235, 1362])).
% 1.96/2.17 tff(11237,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11238,plain,
% 1.96/2.17 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(11239,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11238])).
% 1.96/2.17 tff(11240,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[11239, 11237])).
% 1.96/2.17 tff(11241,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(11242,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[11241, 11240])).
% 1.96/2.17 tff(11243,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11242, 116, 1055, 2247, 1332, 11236, 28])).
% 1.96/2.17 tff(11244,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(11245,plain,
% 1.96/2.17 (~b(elem!1, s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11244, 1362, 2247, 28, 1055, 228, 439])).
% 1.96/2.17 tff(11246,plain,
% 1.96/2.17 (r(elem!1, s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1345, 11245, 1620])).
% 1.96/2.17 tff(11247,plain,
% 1.96/2.17 (~r(s(s(z)), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[5025, 11246, 11232])).
% 1.96/2.17 tff(11248,plain,
% 1.96/2.17 (s(s(z)) = elem!1),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[426, 11247, 11234])).
% 1.96/2.17 tff(11249,plain,
% 1.96/2.17 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[568, 11248])).
% 1.96/2.17 tff(11250,plain,
% 1.96/2.17 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[11248])).
% 1.96/2.17 tff(11251,plain,
% 1.96/2.17 ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2803, 7113])).
% 1.96/2.17 tff(11252,plain,
% 1.96/2.17 (~r(s(z), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[11251, 11230, 2247, 28, 10256])).
% 1.96/2.17 tff(11253,plain,
% 1.96/2.17 (b(s(z), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[172, 11252])).
% 1.96/2.17 tff(11254,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11255,plain,
% 1.96/2.18 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11256,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11255])).
% 1.96/2.18 tff(11257,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11256, 11254])).
% 1.96/2.18 tff(11258,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(11259,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11258, 11257])).
% 1.96/2.18 tff(11260,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11259, 116, 212, 7113, 2442, 174, 249])).
% 1.96/2.18 tff(11261,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(11262,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11261, 11230, 11253, 10256])).
% 1.96/2.18 tff(11263,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[226, 11262])).
% 1.96/2.18 tff(11264,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), elem!1)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11263, 11250])).
% 1.96/2.18 tff(11265,plain,
% 1.96/2.18 (s(s(s(z))) = s(elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11248])).
% 1.96/2.18 tff(11266,plain,
% 1.96/2.18 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11265])).
% 1.96/2.18 tff(11267,plain,
% 1.96/2.18 (b(s(s(s(s(z)))), s(elem!1))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[28, 11266])).
% 1.96/2.18 tff(11268,plain,
% 1.96/2.18 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11265])).
% 1.96/2.18 tff(11269,plain,
% 1.96/2.18 (~b(s(s(s(z))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2791, 116, 2247, 7113, 11230])).
% 1.96/2.18 tff(11270,plain,
% 1.96/2.18 (r(s(s(s(z))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[89, 21, 11269, 56])).
% 1.96/2.18 tff(11271,plain,
% 1.96/2.18 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[8906, 77, 11263, 11270])).
% 1.96/2.18 tff(11272,plain,
% 1.96/2.18 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1146, 11271])).
% 1.96/2.18 tff(11273,plain,
% 1.96/2.18 (b(s(elem!1), s(s(s(s(z)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11272, 11268])).
% 1.96/2.18 tff(11274,plain,
% 1.96/2.18 (s(elem!1) = s(s(s(z)))),
% 1.96/2.18 inference(symmetry,[status(thm)],[11265])).
% 1.96/2.18 tff(11275,plain,
% 1.96/2.18 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11274])).
% 1.96/2.18 tff(11276,plain,
% 1.96/2.18 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.96/2.18 inference(symmetry,[status(thm)],[11275])).
% 1.96/2.18 tff(11277,plain,
% 1.96/2.18 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11248])).
% 1.96/2.18 tff(11278,plain,
% 1.96/2.18 (r(s(s(s(z))), elem!1)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11270, 11277])).
% 1.96/2.18 tff(11279,plain,
% 1.96/2.18 (r(s(elem!1), elem!1)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11278, 11276])).
% 1.96/2.18 tff(11280,plain,
% 1.96/2.18 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[10104, 11279, 228, 3756, 11273, 11267, 11264])).
% 1.96/2.18 tff(11281,plain,
% 1.96/2.18 (b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[885, 11280, 11249])).
% 1.96/2.18 tff(11282,plain,
% 1.96/2.18 ((~(s(s(z)) = elem!1)) | b(elem!1, z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2403, 7113])).
% 1.96/2.18 tff(11283,plain,
% 1.96/2.18 (b(elem!1, z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11282, 11248])).
% 1.96/2.18 tff(11284,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11285,plain,
% 1.96/2.18 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11286,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11285])).
% 1.96/2.18 tff(11287,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11286, 11284])).
% 1.96/2.18 tff(11288,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(11289,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11288, 11287])).
% 1.96/2.18 tff(11290,plain,
% 1.96/2.18 (~b(s(z), s(s(s(s(s(z))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11289, 116, 1055, 11283, 847, 11281])).
% 1.96/2.18 tff(11291,plain,
% 1.96/2.18 (r(s(z), s(s(s(s(s(z))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[870, 21, 1901, 11290])).
% 1.96/2.18 tff(11292,plain,
% 1.96/2.18 (~b(s(s(s(s(s(z))))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4300, 116, 1055, 11283, 11281])).
% 1.96/2.18 tff(11293,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[898, 21, 895, 11292])).
% 1.96/2.18 tff(11294,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11295,plain,
% 1.96/2.18 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11296,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11295])).
% 1.96/2.18 tff(11297,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11296, 11294])).
% 1.96/2.18 tff(11298,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(11299,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11298, 11297])).
% 1.96/2.18 tff(11300,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11299, 77, 155, 11293, 11291])).
% 1.96/2.18 tff(11301,plain,((elem!1 = s(s(s(s(z))))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(11302,plain,
% 1.96/2.18 (elem!1 = s(s(s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11301, 1055, 155, 847, 228, 28, 1620, 2247, 439])).
% 1.96/2.18 tff(11303,plain,
% 1.96/2.18 (~(elem!1 = s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1090, 11302])).
% 1.96/2.18 tff(11304,plain,
% 1.96/2.18 (~(s(s(elem!1)) = elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1097, 11303])).
% 1.96/2.18 tff(11305,plain,
% 1.96/2.18 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[8306, 11302])).
% 1.96/2.18 tff(11306,plain,
% 1.96/2.18 (~(s(s(z)) = elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[836, 11305, 11304])).
% 1.96/2.18 tff(11307,plain,
% 1.96/2.18 (r(s(s(z)), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[426, 11306, 11234])).
% 1.96/2.18 tff(11308,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1746, 2807])).
% 1.96/2.18 tff(11309,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(11310,plain,
% 1.96/2.18 (~(s(s(s(z))) = elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11309, 1620])).
% 1.96/2.18 tff(11311,plain,
% 1.96/2.18 (b(elem!1, s(s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1357, 11302, 28])).
% 1.96/2.18 tff(11312,plain,
% 1.96/2.18 (~b(s(s(s(z))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2767, 11311, 2247, 1055])).
% 1.96/2.18 tff(11313,plain,
% 1.96/2.18 (r(s(s(s(z))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2725, 11312, 11310])).
% 1.96/2.18 tff(11314,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4976, 11313, 11307, 11232])).
% 1.96/2.18 tff(11315,plain,((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(11316,plain,
% 1.96/2.18 (~b(z, elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11315, 11225, 11162, 3406, 2247, 228, 11228, 11226])).
% 1.96/2.18 tff(11317,plain,
% 1.96/2.18 (r(z, elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1044, 11316, 11227])).
% 1.96/2.18 tff(11318,plain,
% 1.96/2.18 (~r(s(s(s(s(z)))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3287, 11317, 228])).
% 1.96/2.18 tff(11319,plain,
% 1.96/2.18 (~(elem!1 = s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3669, 11225])).
% 1.96/2.18 tff(11320,plain,
% 1.96/2.18 (~b(z, s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11175, 11171, 6090])).
% 1.96/2.18 tff(11321,plain,
% 1.96/2.18 (r(z, s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[289, 11320])).
% 1.96/2.18 tff(11322,plain,
% 1.96/2.18 (~r(elem!1, s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[791, 11317, 11321])).
% 1.96/2.18 tff(11323,plain,
% 1.96/2.18 (b(elem!1, s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[633, 11322, 11319])).
% 1.96/2.18 tff(11324,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11325,plain,
% 1.96/2.18 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11326,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11325])).
% 1.96/2.18 tff(11327,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11326, 11324])).
% 1.96/2.18 tff(11328,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(11329,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11328, 11327])).
% 1.96/2.18 tff(11330,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11329, 116, 847, 667, 1725, 249])).
% 1.96/2.18 tff(11331,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(11332,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11331, 11225, 11323, 11199])).
% 1.96/2.18 tff(11333,plain,
% 1.96/2.18 (s(s(s(s(z)))) = elem!1),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1596, 11332, 11318])).
% 1.96/2.18 tff(11334,plain,
% 1.96/2.18 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11333])).
% 1.96/2.18 tff(11335,plain,
% 1.96/2.18 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.96/2.18 inference(symmetry,[status(thm)],[11334])).
% 1.96/2.18 tff(11336,plain,
% 1.96/2.18 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11335])).
% 1.96/2.18 tff(11337,plain,
% 1.96/2.18 ((s(s(z)) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11336, 11163])).
% 1.96/2.18 tff(11338,plain,
% 1.96/2.18 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.96/2.18 inference(symmetry,[status(thm)],[11337])).
% 1.96/2.18 tff(11339,plain,
% 1.96/2.18 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11338])).
% 1.96/2.18 tff(11340,plain,
% 1.96/2.18 (~(s(s(z)) = s(elem!1))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[1202, 11339])).
% 1.96/2.18 tff(11341,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11334])).
% 1.96/2.18 tff(11342,plain,
% 1.96/2.18 (~r(z, s(s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[301, 11321, 6090])).
% 1.96/2.18 tff(11343,plain,
% 1.96/2.18 (b(z, s(s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[267, 21, 11342, 10270])).
% 1.96/2.18 tff(11344,plain,
% 1.96/2.18 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9959, 11343, 2247, 11162, 11321])).
% 1.96/2.18 tff(11345,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1380, 11344])).
% 1.96/2.18 tff(11346,plain,
% 1.96/2.18 (r(s(elem!1), s(s(s(z))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11345, 11341])).
% 1.96/2.18 tff(11347,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11348,plain,
% 1.96/2.18 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11349,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11348])).
% 1.96/2.18 tff(11350,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11349, 11347])).
% 1.96/2.18 tff(11351,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(11352,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11351, 11350])).
% 1.96/2.18 tff(11353,plain,
% 1.96/2.18 (~r(s(elem!1), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11352, 77, 3406, 6090, 11346])).
% 1.96/2.18 tff(11354,plain,
% 1.96/2.18 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.96/2.18 inference(commutativity,[status(thm)],[])).
% 1.96/2.18 tff(11355,plain,
% 1.96/2.18 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = s(elem!1))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11334])).
% 1.96/2.18 tff(11356,plain,
% 1.96/2.18 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(z))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11355, 11354])).
% 1.96/2.18 tff(11357,plain,
% 1.96/2.18 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(z)))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11356])).
% 1.96/2.18 tff(11358,plain,
% 1.96/2.18 (~(s(elem!1) = s(z))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[1901, 11357])).
% 1.96/2.18 tff(11359,plain,
% 1.96/2.18 (b(s(elem!1), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[735, 21, 11358, 11353])).
% 1.96/2.18 tff(11360,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11361,plain,
% 1.96/2.18 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11362,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[11361])).
% 1.96/2.18 tff(11363,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[11362, 11360])).
% 1.96/2.18 tff(11364,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(11365,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[11364, 11363])).
% 1.96/2.18 tff(11366,plain,
% 1.96/2.18 (~b(s(s(z)), s(elem!1))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[11365, 116, 11225, 11323, 11112, 11359])).
% 1.96/2.18 tff(11367,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(11368,plain,
% 1.96/2.18 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11369,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(elem!1)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11368])).
% 1.96/2.19 tff(11370,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[11369, 11367])).
% 1.96/2.19 tff(11371,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(elem!1))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(11372,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(elem!1)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11371, 11370])).
% 1.96/2.19 tff(11373,plain,
% 1.96/2.19 (~r(s(s(z)), s(elem!1))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11372, 77, 11171, 11346])).
% 1.96/2.19 tff(11374,plain,
% 1.96/2.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11375,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(11376,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11375, 11374])).
% 1.96/2.19 tff(11377,plain,
% 1.96/2.19 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11376, 21, 11373])).
% 1.96/2.19 tff(11378,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11377, 11366, 11340])).
% 1.96/2.19 tff(11379,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | b(s(z), z) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11380,plain,
% 1.96/2.19 (~r(s(s(s(s(z)))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11379, 1989, 2247, 1664])).
% 1.96/2.19 tff(11381,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[247, 11380])).
% 1.96/2.19 tff(11382,plain,
% 1.96/2.19 (~b(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2255, 11381, 2247, 11162])).
% 1.96/2.19 tff(11383,plain,
% 1.96/2.19 (r(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[267, 21, 11382, 10270])).
% 1.96/2.19 tff(11384,plain,
% 1.96/2.19 (~r(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[301, 11383, 6090])).
% 1.96/2.19 tff(11385,plain,
% 1.96/2.19 (b(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[289, 11384])).
% 1.96/2.19 tff(11386,plain,
% 1.96/2.19 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11175, 11385, 6090])).
% 1.96/2.19 tff(11387,plain,
% 1.96/2.19 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[105, 11386])).
% 1.96/2.19 tff(11388,plain,
% 1.96/2.19 (~b(z, s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11132, 11387, 2247])).
% 1.96/2.19 tff(11389,plain,
% 1.96/2.19 (~b(s(z), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3422, 11385, 2247, 11162, 11381])).
% 1.96/2.19 tff(11390,plain,
% 1.96/2.19 (r(s(z), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[172, 11389])).
% 1.96/2.19 tff(11391,plain,
% 1.96/2.19 (~r(z, s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10272, 11390, 3406])).
% 1.96/2.19 tff(11392,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1174, 11391, 11388])).
% 1.96/2.19 tff(11393,plain,(b(s(z), z) | (~b(s(s(s(z))), z)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11394,plain,
% 1.96/2.19 (b(s(z), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11393, 2247, 1664])).
% 1.96/2.19 tff(11395,plain,
% 1.96/2.19 (~b(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10652, 11394, 2247])).
% 1.96/2.19 tff(11396,plain,
% 1.96/2.19 (r(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[289, 11395])).
% 1.96/2.19 tff(11397,plain,
% 1.96/2.19 (~r(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[301, 11396, 6090])).
% 1.96/2.19 tff(11398,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[267, 21, 5741, 2486, 10270])).
% 1.96/2.19 tff(11399,plain,(b(z, s(s(s(z)))) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11400,plain,
% 1.96/2.19 (b(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11399, 11397])).
% 1.96/2.19 tff(11401,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11402,plain,
% 1.96/2.19 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11403,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11402])).
% 1.96/2.19 tff(11404,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.96/2.19 inference(transitivity,[status(thm)],[11403, 11401])).
% 1.96/2.19 tff(11405,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(11406,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11405, 11404])).
% 1.96/2.19 tff(11407,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11406, 116, 11394, 2247, 11400, 7113, 11112])).
% 1.96/2.19 tff(11408,plain,((~b(s(s(s(z))), z)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11409,plain,
% 1.96/2.19 (~b(s(s(s(z))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11408, 1664])).
% 1.96/2.19 tff(11410,plain,
% 1.96/2.19 (r(s(s(s(z))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[63, 11409])).
% 1.96/2.19 tff(11411,plain,
% 1.96/2.19 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11129, 3953, 6090])).
% 1.96/2.19 tff(11412,plain,
% 1.96/2.19 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[105, 11411])).
% 1.96/2.19 tff(11413,plain,
% 1.96/2.19 (~r(s(z), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7122, 11410, 6090])).
% 1.96/2.19 tff(11414,plain,
% 1.96/2.19 (b(s(z), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[210, 11413])).
% 1.96/2.19 tff(11415,plain,
% 1.96/2.19 (~b(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10163, 254, 11414])).
% 1.96/2.19 tff(11416,plain,
% 1.96/2.19 (r(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[289, 11415])).
% 1.96/2.19 tff(11417,plain,
% 1.96/2.19 (~r(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[301, 11416, 6090])).
% 1.96/2.19 tff(11418,plain,
% 1.96/2.19 (~r(s(z), s(s(s(s(z)))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3975, 3953, 6090])).
% 1.96/2.19 tff(11419,plain,
% 1.96/2.19 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[325, 11418])).
% 1.96/2.19 tff(11420,plain,
% 1.96/2.19 (~b(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10163, 254, 270])).
% 1.96/2.19 tff(11421,plain,
% 1.96/2.19 (r(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[289, 11420])).
% 1.96/2.19 tff(11422,plain,
% 1.96/2.19 (~r(z, elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7910, 340, 67, 2486, 270, 27, 11421])).
% 1.96/2.19 tff(11423,plain,
% 1.96/2.19 (b(z, elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1044, 11422, 1351])).
% 1.96/2.19 tff(11424,plain,
% 1.96/2.19 (~b(elem!1, z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4732, 11423, 270, 254, 249])).
% 1.96/2.19 tff(11425,plain,
% 1.96/2.19 (r(elem!1, z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[545, 11424, 410])).
% 1.96/2.19 tff(11426,plain,
% 1.96/2.19 (~(s(z) = elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1980, 11422, 254, 249, 270])).
% 1.96/2.19 tff(11427,plain,
% 1.96/2.19 (~(elem!1 = s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[420, 11426])).
% 1.96/2.19 tff(11428,plain,
% 1.96/2.19 ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9402, 7113, 11112])).
% 1.96/2.19 tff(11429,plain,
% 1.96/2.19 (~b(elem!1, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11428, 11423, 270])).
% 1.96/2.19 tff(11430,plain,
% 1.96/2.19 (r(elem!1, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[633, 11429, 11427])).
% 1.96/2.19 tff(11431,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2095, 11430, 11425, 11421])).
% 1.96/2.19 tff(11432,plain,(b(s(z), elem!1) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | r(z, s(s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11433,plain,
% 1.96/2.19 (b(s(z), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11432, 11419, 254, 11414, 11410, 11417, 11412])).
% 1.96/2.19 tff(11434,plain,
% 1.96/2.19 (~(elem!1 = s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1667, 11433, 1664])).
% 1.96/2.19 tff(11435,plain,
% 1.96/2.19 (~r(s(s(s(s(z)))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4668, 77, 3953, 6090])).
% 1.96/2.19 tff(11436,plain,
% 1.96/2.19 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2054, 21, 11435])).
% 1.96/2.19 tff(11437,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11436, 2044])).
% 1.96/2.19 tff(11438,plain,
% 1.96/2.19 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[6779, 116, 11112, 11419, 11437])).
% 1.96/2.19 tff(11439,plain,
% 1.96/2.19 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[226, 11438])).
% 1.96/2.19 tff(11440,plain,
% 1.96/2.19 (~r(s(s(s(z))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[5905, 11439, 3953])).
% 1.96/2.19 tff(11441,plain,
% 1.96/2.19 (~(s(s(s(z))) = elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11309, 11434])).
% 1.96/2.19 tff(11442,plain,
% 1.96/2.19 (b(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11399, 11417])).
% 1.96/2.19 tff(11443,plain,
% 1.96/2.19 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(symmetry,[status(thm)],[3221])).
% 1.96/2.19 tff(11444,plain,
% 1.96/2.19 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11443])).
% 1.96/2.19 tff(11445,plain,
% 1.96/2.19 (b(elem!1, z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11282, 370])).
% 1.96/2.19 tff(11446,plain,
% 1.96/2.19 (~r(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9083, 370, 9080])).
% 1.96/2.19 tff(11447,plain,
% 1.96/2.19 (b(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2725, 11446, 2688])).
% 1.96/2.19 tff(11448,plain,
% 1.96/2.19 (~b(elem!1, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9532, 11447, 255, 11445])).
% 1.96/2.19 tff(11449,plain,
% 1.96/2.19 (~b(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11448, 11444])).
% 1.96/2.19 tff(11450,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[27, 11449])).
% 1.96/2.19 tff(11451,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (s(s(s(z))) = elem!1) | r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11452,plain,
% 1.96/2.19 (~(s(s(z)) = elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11451, 11412, 11442, 11441, 11440])).
% 1.96/2.19 tff(11453,plain,
% 1.96/2.19 (~b(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10163, 270, 254])).
% 1.96/2.19 tff(11454,plain,
% 1.96/2.19 (~r(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[6099, 270, 847, 1052, 518])).
% 1.96/2.19 tff(11455,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[289, 11454, 11453])).
% 1.96/2.19 tff(11456,plain,((~b(s(z), z)) | (~b(s(z), elem!1)) | r(z, elem!1) | (z = elem!1) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11457,plain,
% 1.96/2.19 (r(z, elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11456, 518, 254, 270, 847])).
% 1.96/2.19 tff(11458,plain,
% 1.96/2.19 (~b(z, s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10827, 518, 67, 11421, 270, 847, 1620])).
% 1.96/2.19 tff(11459,plain,
% 1.96/2.19 (r(z, s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1174, 11458])).
% 1.96/2.19 tff(11460,plain,
% 1.96/2.19 (~r(s(s(z)), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10758, 11459, 11457])).
% 1.96/2.19 tff(11461,plain,
% 1.96/2.19 (~r(elem!1, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[791, 11457, 11421])).
% 1.96/2.19 tff(11462,plain,
% 1.96/2.19 (b(elem!1, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[633, 11461, 3670])).
% 1.96/2.19 tff(11463,plain,
% 1.96/2.19 ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7082, 11112])).
% 1.96/2.19 tff(11464,plain,
% 1.96/2.19 (~b(s(s(z)), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11463, 11462, 847])).
% 1.96/2.19 tff(11465,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[426, 11464, 11460, 422])).
% 1.96/2.19 tff(11466,plain,((z = elem!1) | (s(s(z)) = elem!1) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11467,plain,
% 1.96/2.19 (z = elem!1),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11466, 11452, 11433, 11410, 11414, 11434, 254])).
% 1.96/2.19 tff(11468,plain,
% 1.96/2.19 (s(z) = s(elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11467])).
% 1.96/2.19 tff(11469,plain,
% 1.96/2.19 (s(s(z)) = s(s(elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11468])).
% 1.96/2.19 tff(11470,plain,
% 1.96/2.19 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11469])).
% 1.96/2.19 tff(11471,plain,
% 1.96/2.19 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.96/2.19 inference(transitivity,[status(thm)],[11470, 7690])).
% 1.96/2.19 tff(11472,plain,
% 1.96/2.19 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11471])).
% 1.96/2.19 tff(11473,plain,
% 1.96/2.19 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[100, 11472])).
% 1.96/2.19 tff(11474,plain,
% 1.96/2.19 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11469])).
% 1.96/2.19 tff(11475,plain,
% 1.96/2.19 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11474])).
% 1.96/2.19 tff(11476,plain,
% 1.96/2.19 (elem!1 = z),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[445, 11467])).
% 1.96/2.19 tff(11477,plain,
% 1.96/2.19 (b(s(s(z)), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7117, 11476])).
% 1.96/2.19 tff(11478,plain,
% 1.96/2.19 (~r(elem!1, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2488, 11476, 11417])).
% 1.96/2.19 tff(11479,plain,
% 1.96/2.19 (b(elem!1, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1345, 11478, 11434])).
% 1.96/2.19 tff(11480,plain,
% 1.96/2.19 (~b(s(s(s(z))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1340, 11479, 11412, 11477])).
% 1.96/2.19 tff(11481,plain,
% 1.96/2.19 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11480, 11475])).
% 1.96/2.19 tff(11482,plain,
% 1.96/2.19 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11469])).
% 1.96/2.19 tff(11483,plain,
% 1.96/2.19 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11482])).
% 1.96/2.19 tff(11484,plain,
% 1.96/2.19 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11440, 11483])).
% 1.96/2.19 tff(11485,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[664, 11484, 11481, 11473])).
% 1.96/2.19 tff(11486,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11487,plain,
% 1.96/2.19 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11486, 254, 1664])).
% 1.96/2.19 tff(11488,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3951, 11487])).
% 1.96/2.19 tff(11489,plain,
% 1.96/2.19 (~r(s(z), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7122, 67, 292])).
% 1.96/2.19 tff(11490,plain,
% 1.96/2.19 (b(s(z), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[210, 11489])).
% 1.96/2.19 tff(11491,plain,
% 1.96/2.19 (~(elem!1 = z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[409, 340, 11490])).
% 1.96/2.19 tff(11492,plain,
% 1.96/2.19 (~b(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10163, 254, 11490])).
% 1.96/2.19 tff(11493,plain,
% 1.96/2.19 (r(z, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[289, 11492])).
% 1.96/2.19 tff(11494,plain,
% 1.96/2.19 (~(z = elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[445, 11491])).
% 1.96/2.19 tff(11495,plain,
% 1.96/2.19 (~r(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[301, 11493, 292])).
% 1.96/2.19 tff(11496,plain,
% 1.96/2.19 (r(z, elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9411, 2235, 292, 67, 340, 11492])).
% 1.96/2.19 tff(11497,plain,
% 1.96/2.19 (~r(s(z), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3295, 11496, 11493])).
% 1.96/2.19 tff(11498,plain,
% 1.96/2.19 (s(z) = elem!1),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[357, 11497, 340])).
% 1.96/2.19 tff(11499,plain,
% 1.96/2.19 (s(s(z)) = s(elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11498])).
% 1.96/2.19 tff(11500,plain,
% 1.96/2.19 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11499])).
% 1.96/2.19 tff(11501,plain,
% 1.96/2.19 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11498])).
% 1.96/2.19 tff(11502,plain,
% 1.96/2.19 (b(s(z), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[172, 11117])).
% 1.96/2.19 tff(11503,plain,
% 1.96/2.19 (b(elem!1, s(s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11502, 11501])).
% 1.96/2.19 tff(11504,plain,
% 1.96/2.19 (b(elem!1, s(elem!1))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11503, 11500])).
% 1.96/2.19 tff(11505,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2016, 11498, 28])).
% 1.96/2.19 tff(11506,plain,
% 1.96/2.19 (s(s(s(z))) = s(s(elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11499])).
% 1.96/2.19 tff(11507,plain,
% 1.96/2.19 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11506])).
% 1.96/2.19 tff(11508,plain,
% 1.96/2.19 (b(z, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11399, 11495])).
% 1.96/2.19 tff(11509,plain,
% 1.96/2.19 (b(z, s(s(elem!1)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11508, 11507])).
% 1.96/2.19 tff(11510,plain,
% 1.96/2.19 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11498])).
% 1.96/2.19 tff(11511,plain,
% 1.96/2.19 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11510])).
% 1.96/2.19 tff(11512,plain,
% 1.96/2.19 (~(s(s(elem!1)) = elem!1)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[566, 11511])).
% 1.96/2.19 tff(11513,plain,
% 1.96/2.19 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11506])).
% 1.96/2.19 tff(11514,plain,
% 1.96/2.19 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11513])).
% 1.96/2.19 tff(11515,plain,
% 1.96/2.19 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11498])).
% 1.96/2.19 tff(11516,plain,
% 1.96/2.19 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(z))), elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11515])).
% 1.96/2.19 tff(11517,plain,
% 1.96/2.19 (~r(s(s(s(z))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[10803, 11496, 67, 11493])).
% 1.96/2.19 tff(11518,plain,
% 1.96/2.19 (~r(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11517, 11516])).
% 1.96/2.19 tff(11519,plain,
% 1.96/2.19 (~r(s(s(elem!1)), elem!1)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11518, 11514])).
% 1.96/2.19 tff(11520,plain,
% 1.96/2.19 (b(s(s(elem!1)), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[743, 11519, 11512])).
% 1.96/2.19 tff(11521,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11522,plain,
% 1.96/2.19 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11523,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11522])).
% 1.96/2.19 tff(11524,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[11523, 11521])).
% 1.96/2.19 tff(11525,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(11526,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11525, 11524])).
% 1.96/2.19 tff(11527,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11526, 116, 11520, 11509, 11505, 254, 11504])).
% 1.96/2.19 tff(11528,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), elem!1) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11529,plain,
% 1.96/2.19 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11528, 340, 28, 254, 67, 292])).
% 1.96/2.19 tff(11530,plain,
% 1.96/2.19 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[105, 11529])).
% 1.96/2.19 tff(11531,plain,
% 1.96/2.19 (~r(z, elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7910, 11530, 67, 11495, 11490, 340, 11493])).
% 1.96/2.19 tff(11532,plain,
% 1.96/2.19 (b(z, elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1044, 11531, 11494])).
% 1.96/2.19 tff(11533,plain,
% 1.96/2.19 (~b(elem!1, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11428, 11532, 11490])).
% 1.96/2.19 tff(11534,plain,
% 1.96/2.19 (~(s(z) = elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4796, 11532, 11492])).
% 1.96/2.19 tff(11535,plain,
% 1.96/2.19 (~(elem!1 = s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[420, 11534])).
% 1.96/2.19 tff(11536,plain,
% 1.96/2.19 (r(elem!1, s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[633, 11535, 11533])).
% 1.96/2.19 tff(11537,plain,
% 1.96/2.19 (~r(elem!1, z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2095, 11536, 11493])).
% 1.96/2.19 tff(11538,plain,
% 1.96/2.19 (b(elem!1, z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[545, 11537, 11491])).
% 1.96/2.19 tff(11539,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9409, 116, 11532, 11538, 11490, 7113, 11112])).
% 1.96/2.19 tff(11540,plain,(b(s(z), elem!1) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(11541,plain,
% 1.96/2.19 (b(s(z), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11540, 11488, 11410, 254, 6090])).
% 1.96/2.19 tff(11542,plain,
% 1.96/2.19 (~(elem!1 = s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1667, 11541, 1664])).
% 1.96/2.19 tff(11543,plain,
% 1.96/2.19 (s(s(z)) = elem!1),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11466, 518, 847, 67, 270, 1620, 254])).
% 1.96/2.19 tff(11544,plain,
% 1.96/2.19 (s(s(s(z))) = s(elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11543])).
% 1.96/2.19 tff(11545,plain,
% 1.96/2.19 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11544])).
% 1.96/2.19 tff(11546,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11545])).
% 1.96/2.19 tff(11547,plain,
% 1.96/2.19 (b(s(s(elem!1)), z)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[254, 11546])).
% 1.96/2.19 tff(11548,plain,
% 1.96/2.19 (~(s(s(elem!1)) = elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[529, 11543, 518])).
% 1.96/2.19 tff(11549,plain,
% 1.96/2.19 (s(elem!1) = s(s(s(z)))),
% 1.96/2.19 inference(symmetry,[status(thm)],[11544])).
% 1.96/2.19 tff(11550,plain,
% 1.96/2.19 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11549])).
% 1.96/2.19 tff(11551,plain,
% 1.96/2.19 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.96/2.19 inference(symmetry,[status(thm)],[11550])).
% 1.96/2.19 tff(11552,plain,
% 1.96/2.19 (~r(s(s(s(z))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7618, 11459, 67])).
% 1.96/2.19 tff(11553,plain,
% 1.96/2.19 (~r(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9083, 11552, 11543])).
% 1.96/2.19 tff(11554,plain,
% 1.96/2.19 (b(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2725, 11553, 11310])).
% 1.96/2.19 tff(11555,plain,
% 1.96/2.19 (b(s(elem!1), elem!1)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11554, 11551])).
% 1.96/2.19 tff(11556,plain,
% 1.96/2.19 (b(s(s(elem!1)), s(elem!1))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3257, 11543, 28])).
% 1.96/2.19 tff(11557,plain,
% 1.96/2.19 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[556])).
% 1.96/2.19 tff(11558,plain,
% 1.96/2.19 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 1.96/2.19 inference(symmetry,[status(thm)],[11557])).
% 1.96/2.19 tff(11559,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11560,plain,
% 1.96/2.19 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11561,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11560])).
% 1.96/2.19 tff(11562,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[11561, 11559])).
% 1.96/2.19 tff(11563,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(11564,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11563, 11562])).
% 1.96/2.19 tff(11565,plain,
% 1.96/2.19 (~b(s(s(elem!1)), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[11564, 116, 616, 847, 667])).
% 1.96/2.19 tff(11566,plain,
% 1.96/2.19 (r(s(s(elem!1)), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[808, 11565])).
% 1.96/2.19 tff(11567,plain,
% 1.96/2.19 (~r(z, s(s(elem!1)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3185, 11566, 293])).
% 1.96/2.19 tff(11568,plain,
% 1.96/2.19 (b(z, s(s(elem!1)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[514, 11567])).
% 1.96/2.19 tff(11569,plain,
% 1.96/2.19 (b(z, s(s(s(s(z)))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[11568, 11558])).
% 1.96/2.19 tff(11570,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11571,plain,
% 1.96/2.19 (((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(11572,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[11571])).
% 1.96/2.19 tff(11573,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.96/2.19 inference(transitivity,[status(thm)],[11572, 11570])).
% 1.96/2.19 tff(11574,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.96/2.20 inference(quant_inst,[status(thm)],[])).
% 1.96/2.20 tff(11575,plain,
% 1.96/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.96/2.20 inference(modus_ponens,[status(thm)],[11574, 11573])).
% 1.96/2.20 tff(11576,plain,
% 1.96/2.20 ($false),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[11575, 116, 537, 616, 846, 1877, 1176])).
% 1.96/2.20 tff(11577,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.20 tff(11578,plain,
% 1.96/2.20 (~b(z, s(s(s(s(z)))))),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[11577, 616, 1877, 11445, 846])).
% 1.96/2.20 tff(11579,plain,
% 1.96/2.20 ($false),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[11578, 11569])).
% 1.96/2.20 tff(11580,plain,((~b(s(s(elem!1)), elem!1)) | (~(s(s(z)) = elem!1)) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11581,plain,
% 2.04/2.20 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11580, 11543, 11421, 11556, 11555, 847, 11462])).
% 2.04/2.20 tff(11582,plain,
% 2.04/2.20 (r(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[743, 11581, 11548])).
% 2.04/2.20 tff(11583,plain,
% 2.04/2.20 (~r(z, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3440, 11582, 11457])).
% 2.04/2.20 tff(11584,plain,
% 2.04/2.20 (b(z, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[514, 11583])).
% 2.04/2.20 tff(11585,plain,
% 2.04/2.20 (b(elem!1, z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11282, 11543])).
% 2.04/2.20 tff(11586,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11587,plain,
% 2.04/2.20 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11588,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11587])).
% 2.04/2.20 tff(11589,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[11588, 11586])).
% 2.04/2.20 tff(11590,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(11591,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11590, 11589])).
% 2.04/2.20 tff(11592,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11591, 116, 11585, 847, 270, 11584, 11547])).
% 2.04/2.20 tff(11593,plain,((z = elem!1) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11594,plain,
% 2.04/2.20 (z = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11593, 11541, 11414, 254, 11410, 11488, 11542])).
% 2.04/2.20 tff(11595,plain,
% 2.04/2.20 (s(z) = s(elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11594])).
% 2.04/2.20 tff(11596,plain,
% 2.04/2.20 (s(s(z)) = s(s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11595])).
% 2.04/2.20 tff(11597,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11596])).
% 2.04/2.20 tff(11598,plain,
% 2.04/2.20 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[1785])).
% 2.04/2.20 tff(11599,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.04/2.20 tff(11600,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11599, 11598])).
% 2.04/2.20 tff(11601,plain,
% 2.04/2.20 (r(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[664, 11600, 9822])).
% 2.04/2.20 tff(11602,plain,
% 2.04/2.20 (b(s(s(z)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7117, 1713])).
% 2.04/2.20 tff(11603,plain,
% 2.04/2.20 (~b(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11463, 11602, 847])).
% 2.04/2.20 tff(11604,plain,
% 2.04/2.20 (~r(s(s(elem!1)), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10641, 442, 67, 847])).
% 2.04/2.20 tff(11605,plain,
% 2.04/2.20 (b(s(s(elem!1)), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[808, 11604])).
% 2.04/2.20 tff(11606,plain,
% 2.04/2.20 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7291, 11605, 11603])).
% 2.04/2.20 tff(11607,plain,
% 2.04/2.20 (~(elem!1 = s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2182, 11606])).
% 2.04/2.20 tff(11608,plain,
% 2.04/2.20 ((~(elem!1 = z)) | b(s(s(elem!1)), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7170, 7113])).
% 2.04/2.20 tff(11609,plain,
% 2.04/2.20 (b(s(s(elem!1)), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11608, 1713])).
% 2.04/2.20 tff(11610,plain,
% 2.04/2.20 (b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11609, 8084])).
% 2.04/2.20 tff(11611,plain,
% 2.04/2.20 (~b(elem!1, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3698, 11610, 847, 11605])).
% 2.04/2.20 tff(11612,plain,
% 2.04/2.20 (r(elem!1, s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1892, 11611, 11607])).
% 2.04/2.20 tff(11613,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11614,plain,
% 2.04/2.20 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11615,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11614])).
% 2.04/2.20 tff(11616,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[11615, 11613])).
% 2.04/2.20 tff(11617,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(11618,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11617, 11616])).
% 2.04/2.20 tff(11619,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11618, 77, 11612, 10546, 11601])).
% 2.04/2.20 tff(11620,plain,((~(z = elem!1)) | (~b(s(z), elem!1)) | b(s(s(s(z))), s(s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11621,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11620, 11594, 11541, 11410])).
% 2.04/2.20 tff(11622,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11621, 11597])).
% 2.04/2.20 tff(11623,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11594])).
% 2.04/2.20 tff(11624,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[254, 11623])).
% 2.04/2.20 tff(11625,plain,
% 2.04/2.20 (elem!1 = z),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[445, 11594])).
% 2.04/2.20 tff(11626,plain,
% 2.04/2.20 (~r(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2488, 11625, 11417])).
% 2.04/2.20 tff(11627,plain,
% 2.04/2.20 (b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1345, 11626, 11542])).
% 2.04/2.20 tff(11628,plain,
% 2.04/2.20 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11594])).
% 2.04/2.20 tff(11629,plain,
% 2.04/2.20 (b(s(s(elem!1)), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11608, 11625])).
% 2.04/2.20 tff(11630,plain,
% 2.04/2.20 (b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11629, 11628])).
% 2.04/2.20 tff(11631,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11632,plain,
% 2.04/2.20 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11633,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11632])).
% 2.04/2.20 tff(11634,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[11633, 11631])).
% 2.04/2.20 tff(11635,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(11636,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11635, 11634])).
% 2.04/2.20 tff(11637,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11636, 116, 11630, 11627, 11488, 11624, 11622])).
% 2.04/2.20 tff(11638,plain,((~b(s(s(s(s(z)))), z)) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11639,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11638, 1664])).
% 2.04/2.20 tff(11640,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[247, 11639])).
% 2.04/2.20 tff(11641,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10693, 77, 11410, 11640])).
% 2.04/2.20 tff(11642,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1146, 11641])).
% 2.04/2.20 tff(11643,plain,
% 2.04/2.20 (~(elem!1 = z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[409, 340, 7124])).
% 2.04/2.20 tff(11644,plain,
% 2.04/2.20 (~(z = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[445, 11643])).
% 2.04/2.20 tff(11645,plain,
% 2.04/2.20 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11175, 271, 292])).
% 2.04/2.20 tff(11646,plain,
% 2.04/2.20 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[105, 11645])).
% 2.04/2.20 tff(11647,plain,
% 2.04/2.20 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10903, 11646, 1177, 28])).
% 2.04/2.20 tff(11648,plain,
% 2.04/2.20 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10854, 271, 292, 270])).
% 2.04/2.20 tff(11649,plain,
% 2.04/2.20 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1380, 11648])).
% 2.04/2.20 tff(11650,plain,
% 2.04/2.20 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10893, 11649, 28, 11646])).
% 2.04/2.20 tff(11651,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[149, 11650, 11647])).
% 2.04/2.20 tff(11652,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11653,plain,
% 2.04/2.20 (~b(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11652, 8775, 10695, 292, 11490])).
% 2.04/2.20 tff(11654,plain,
% 2.04/2.20 (r(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[289, 11653])).
% 2.04/2.20 tff(11655,plain,
% 2.04/2.20 (~r(s(z), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3295, 448, 11654])).
% 2.04/2.20 tff(11656,plain,
% 2.04/2.20 (s(z) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[357, 11655, 340])).
% 2.04/2.20 tff(11657,plain,
% 2.04/2.20 (s(s(z)) = s(elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11656])).
% 2.04/2.20 tff(11658,plain,
% 2.04/2.20 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11657])).
% 2.04/2.20 tff(11659,plain,
% 2.04/2.20 (b(elem!1, z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1458, 11656, 11490])).
% 2.04/2.20 tff(11660,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3287, 448, 228])).
% 2.04/2.20 tff(11661,plain,
% 2.04/2.20 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11656])).
% 2.04/2.20 tff(11662,plain,
% 2.04/2.20 (b(s(s(z)), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11112, 11661])).
% 2.04/2.20 tff(11663,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3343, 11662, 292, 340, 11654, 11660, 11659, 448])).
% 2.04/2.20 tff(11664,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[226, 11663])).
% 2.04/2.20 tff(11665,plain,
% 2.04/2.20 (~r(z, s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2549, 11664, 228])).
% 2.04/2.20 tff(11666,plain,
% 2.04/2.20 (b(z, s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1174, 11665])).
% 2.04/2.20 tff(11667,plain,
% 2.04/2.20 (b(z, s(elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11666, 11658])).
% 2.04/2.20 tff(11668,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1531, 11656])).
% 2.04/2.20 tff(11669,plain,
% 2.04/2.20 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1584, 11668])).
% 2.04/2.20 tff(11670,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1596, 11669, 11660])).
% 2.04/2.20 tff(11671,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2016, 11656, 8775])).
% 2.04/2.20 tff(11672,plain,
% 2.04/2.20 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11656])).
% 2.04/2.20 tff(11673,plain,
% 2.04/2.20 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11672])).
% 2.04/2.20 tff(11674,plain,
% 2.04/2.20 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[566, 11673])).
% 2.04/2.20 tff(11675,plain,
% 2.04/2.20 (s(s(s(z))) = s(s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11657])).
% 2.04/2.20 tff(11676,plain,
% 2.04/2.20 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11675])).
% 2.04/2.20 tff(11677,plain,
% 2.04/2.20 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11676])).
% 2.04/2.20 tff(11678,plain,
% 2.04/2.20 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11656])).
% 2.04/2.20 tff(11679,plain,
% 2.04/2.20 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(z))), elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11678])).
% 2.04/2.20 tff(11680,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10803, 448, 67, 11654])).
% 2.04/2.20 tff(11681,plain,
% 2.04/2.20 (~r(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11680, 11679])).
% 2.04/2.20 tff(11682,plain,
% 2.04/2.20 (~r(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11681, 11677])).
% 2.04/2.20 tff(11683,plain,
% 2.04/2.20 (b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[743, 11682, 11674])).
% 2.04/2.20 tff(11684,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11685,plain,
% 2.04/2.20 (((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(11686,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11685])).
% 2.04/2.20 tff(11687,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[11686, 11684])).
% 2.04/2.20 tff(11688,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(11689,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11688, 11687])).
% 2.04/2.20 tff(11690,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11689, 116, 537, 616, 2023, 1725, 8835])).
% 2.04/2.20 tff(11691,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11692,plain,
% 2.04/2.20 (~b(z, s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11691, 11683, 11671, 11670, 11659])).
% 2.04/2.20 tff(11693,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11692, 11667])).
% 2.04/2.20 tff(11694,plain,((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | b(s(z), elem!1) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11695,plain,
% 2.04/2.20 (~r(z, elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11694, 340, 292, 3552, 64])).
% 2.04/2.20 tff(11696,plain,
% 2.04/2.20 (b(z, elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1044, 11695, 11644])).
% 2.04/2.20 tff(11697,plain,
% 2.04/2.20 ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1311, 7113, 11112])).
% 2.04/2.20 tff(11698,plain,
% 2.04/2.20 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11697, 11696, 7124])).
% 2.04/2.20 tff(11699,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3961, 3552, 64])).
% 2.04/2.20 tff(11700,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3951, 11699])).
% 2.04/2.20 tff(11701,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10693, 77, 64, 3552])).
% 2.04/2.20 tff(11702,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1146, 11701])).
% 2.04/2.20 tff(11703,plain,
% 2.04/2.20 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9448, 11695, 57, 11700, 340])).
% 2.04/2.20 tff(11704,plain,
% 2.04/2.20 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[105, 11703])).
% 2.04/2.20 tff(11705,plain,
% 2.04/2.20 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10903, 11704, 11702, 11700])).
% 2.04/2.20 tff(11706,plain,
% 2.04/2.20 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[149, 11705])).
% 2.04/2.20 tff(11707,plain,
% 2.04/2.20 (~b(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11652, 11700, 11702, 292, 7124])).
% 2.04/2.20 tff(11708,plain,
% 2.04/2.20 (r(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[289, 11707])).
% 2.04/2.20 tff(11709,plain,
% 2.04/2.20 (~b(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11428, 11696, 7124])).
% 2.04/2.20 tff(11710,plain,
% 2.04/2.20 (~(s(z) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4796, 11696, 11707])).
% 2.04/2.20 tff(11711,plain,
% 2.04/2.20 (~(elem!1 = s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[420, 11710])).
% 2.04/2.20 tff(11712,plain,
% 2.04/2.20 (r(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[633, 11711, 11709])).
% 2.04/2.20 tff(11713,plain,
% 2.04/2.20 (~r(elem!1, z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2095, 11712, 11708])).
% 2.04/2.20 tff(11714,plain,
% 2.04/2.20 (b(elem!1, z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[545, 11713, 11643])).
% 2.04/2.20 tff(11715,plain,
% 2.04/2.20 (~b(s(s(z)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8043, 11714, 11696])).
% 2.04/2.20 tff(11716,plain,
% 2.04/2.20 (r(s(z), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[357, 11710, 340])).
% 2.04/2.20 tff(11717,plain,
% 2.04/2.20 (~r(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[368, 11716, 292])).
% 2.04/2.20 tff(11718,plain,
% 2.04/2.20 (~r(s(z), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8040, 11715, 7124, 11708, 340, 11716, 11717, 11695, 57])).
% 2.04/2.20 tff(11719,plain,
% 2.04/2.20 (b(s(z), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[172, 11718])).
% 2.04/2.20 tff(11720,plain,
% 2.04/2.20 (~(s(s(z)) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[376, 11719, 340])).
% 2.04/2.20 tff(11721,plain,
% 2.04/2.20 (r(s(s(z)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[426, 11720, 11715])).
% 2.04/2.20 tff(11722,plain,
% 2.04/2.20 (~r(elem!1, s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[437, 11721, 11706])).
% 2.04/2.20 tff(11723,plain,
% 2.04/2.20 (elem!1 = s(s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1068, 11722, 11698])).
% 2.04/2.20 tff(11724,plain,
% 2.04/2.20 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11723])).
% 2.04/2.20 tff(11725,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 2.04/2.20 inference(symmetry,[status(thm)],[11724])).
% 2.04/2.20 tff(11726,plain,
% 2.04/2.20 ((~b(s(s(s(s(z)))), z)) <=> (~b(elem!1, z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11725])).
% 2.04/2.20 tff(11727,plain,
% 2.04/2.20 (~b(elem!1, z)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[239, 11726])).
% 2.04/2.20 tff(11728,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11714, 11727])).
% 2.04/2.20 tff(11729,plain,(b(s(z), elem!1) | b(s(s(s(s(z)))), z) | b(s(s(s(z))), z) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11730,plain,
% 2.04/2.20 (b(s(z), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11729, 11639, 11409, 6090])).
% 2.04/2.20 tff(11731,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1667, 11730, 1664])).
% 2.04/2.20 tff(11732,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3961, 11640, 11410])).
% 2.04/2.20 tff(11733,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3951, 11732])).
% 2.04/2.20 tff(11734,plain,
% 2.04/2.20 (~b(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11652, 11733, 11642, 6090, 11414])).
% 2.04/2.20 tff(11735,plain,
% 2.04/2.20 (r(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[289, 11734])).
% 2.04/2.20 tff(11736,plain,
% 2.04/2.20 (r(z, elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10755, 518, 67, 228, 8775, 847])).
% 2.04/2.20 tff(11737,plain,
% 2.04/2.20 (~r(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[791, 11736, 293])).
% 2.04/2.20 tff(11738,plain,
% 2.04/2.20 (b(elem!1, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[633, 11737, 3670])).
% 2.04/2.20 tff(11739,plain,
% 2.04/2.20 (~b(s(s(z)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11463, 11738, 847])).
% 2.04/2.20 tff(11740,plain,
% 2.04/2.20 (~b(z, s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10827, 518, 67, 293, 270, 847, 1620])).
% 2.04/2.20 tff(11741,plain,
% 2.04/2.20 (r(z, s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1174, 11740])).
% 2.04/2.20 tff(11742,plain,
% 2.04/2.20 (~r(s(s(z)), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[10758, 11741, 11736])).
% 2.04/2.20 tff(11743,plain,
% 2.04/2.20 (s(s(z)) = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[426, 11742, 11739])).
% 2.04/2.20 tff(11744,plain,
% 2.04/2.20 (b(s(s(elem!1)), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3257, 11743, 8775])).
% 2.04/2.20 tff(11745,plain,
% 2.04/2.20 (s(s(s(z))) = s(elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11743])).
% 2.04/2.20 tff(11746,plain,
% 2.04/2.20 (s(elem!1) = s(s(s(z)))),
% 2.04/2.20 inference(symmetry,[status(thm)],[11745])).
% 2.04/2.20 tff(11747,plain,
% 2.04/2.20 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11746])).
% 2.04/2.20 tff(11748,plain,
% 2.04/2.20 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.04/2.20 inference(symmetry,[status(thm)],[11747])).
% 2.04/2.20 tff(11749,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7618, 11741, 67])).
% 2.04/2.20 tff(11750,plain,
% 2.04/2.20 (~r(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9083, 11743, 11749])).
% 2.04/2.20 tff(11751,plain,
% 2.04/2.20 (b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2725, 11750, 11310])).
% 2.04/2.20 tff(11752,plain,
% 2.04/2.20 (b(s(elem!1), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11751, 11748])).
% 2.04/2.20 tff(11753,plain,
% 2.04/2.20 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11745])).
% 2.04/2.20 tff(11754,plain,
% 2.04/2.20 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[11753])).
% 2.04/2.20 tff(11755,plain,
% 2.04/2.20 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11754])).
% 2.04/2.20 tff(11756,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(symmetry,[status(thm)],[11755])).
% 2.04/2.20 tff(11757,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3287, 11736, 228])).
% 2.04/2.20 tff(11758,plain,
% 2.04/2.20 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[529, 11743, 518])).
% 2.04/2.20 tff(11759,plain,
% 2.04/2.20 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[836, 11743, 11758])).
% 2.04/2.20 tff(11760,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[8306, 11759])).
% 2.04/2.20 tff(11761,plain,
% 2.04/2.20 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1584, 11760])).
% 2.04/2.20 tff(11762,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1596, 11761, 11757])).
% 2.04/2.20 tff(11763,plain,
% 2.04/2.20 (b(s(s(elem!1)), elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[11762, 11756])).
% 2.04/2.20 tff(11764,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11580, 11763, 11752, 293, 11744, 11743, 847, 11738])).
% 2.04/2.20 tff(11765,plain,((z = elem!1) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(11766,plain,
% 2.04/2.20 (z = elem!1),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[11765, 11735, 11730, 11410, 11640, 11414, 11731])).
% 2.04/2.20 tff(11767,plain,
% 2.04/2.20 (s(z) = s(elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11766])).
% 2.04/2.20 tff(11768,plain,
% 2.04/2.20 (s(s(z)) = s(s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[11767])).
% 2.04/2.20 tff(11769,plain,
% 2.04/2.20 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11767, 11768])).
% 2.04/2.21 tff(11770,plain,
% 2.04/2.21 (elem!1 = z),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[445, 11766])).
% 2.04/2.21 tff(11771,plain,
% 2.04/2.21 (b(s(s(z)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7117, 11770])).
% 2.04/2.21 tff(11772,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11620, 11766, 11730, 11410])).
% 2.04/2.21 tff(11773,plain,
% 2.04/2.21 (~r(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[301, 11735, 6090])).
% 2.04/2.21 tff(11774,plain,
% 2.04/2.21 (~r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2488, 11770, 11773])).
% 2.04/2.21 tff(11775,plain,
% 2.04/2.21 (b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1345, 11774, 11731])).
% 2.04/2.21 tff(11776,plain,
% 2.04/2.21 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1340, 11775, 11772, 11771])).
% 2.04/2.21 tff(11777,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[105, 11776])).
% 2.04/2.21 tff(11778,plain,
% 2.04/2.21 (~r(s(z), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2319, 11777, 6090])).
% 2.04/2.21 tff(11779,plain,
% 2.04/2.21 (b(s(z), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[172, 11778])).
% 2.04/2.21 tff(11780,plain,
% 2.04/2.21 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11779, 11769])).
% 2.04/2.21 tff(11781,plain,
% 2.04/2.21 (b(s(elem!1), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6119, 11766, 11730])).
% 2.04/2.21 tff(11782,plain,
% 2.04/2.21 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11766])).
% 2.04/2.21 tff(11783,plain,
% 2.04/2.21 (b(s(s(elem!1)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11608, 11770])).
% 2.04/2.21 tff(11784,plain,
% 2.04/2.21 (b(s(s(elem!1)), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11783, 11782])).
% 2.04/2.21 tff(11785,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11786,plain,
% 2.04/2.21 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11787,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11786])).
% 2.04/2.21 tff(11788,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[11787, 11785])).
% 2.04/2.21 tff(11789,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(11790,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11789, 11788])).
% 2.04/2.21 tff(11791,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11790, 116, 11784, 11775, 11781, 11780, 11642])).
% 2.04/2.21 tff(11792,plain,(b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11793,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11794,plain,
% 2.04/2.21 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11795,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11794])).
% 2.04/2.21 tff(11796,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[11795, 11793])).
% 2.04/2.21 tff(11797,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(11798,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11797, 11796])).
% 2.04/2.21 tff(11799,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11798, 116, 271, 2247, 7113, 11792, 11112])).
% 2.04/2.21 tff(11800,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11801,plain,
% 2.04/2.21 (~b(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11800, 271])).
% 2.04/2.21 tff(11802,plain,
% 2.04/2.21 (r(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[63, 11801])).
% 2.04/2.21 tff(11803,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2136, 11802, 155])).
% 2.04/2.21 tff(11804,plain,
% 2.04/2.21 ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9379, 7113, 11112])).
% 2.04/2.21 tff(11805,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11804, 271, 11792])).
% 2.04/2.21 tff(11806,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[402, 21, 135, 11805, 11803])).
% 2.04/2.21 tff(11807,plain,((~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11808,plain,
% 2.04/2.21 (~b(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11807, 155])).
% 2.04/2.21 tff(11809,plain,
% 2.04/2.21 (r(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[289, 11808])).
% 2.04/2.21 tff(11810,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 2.04/2.21 tff(11811,plain,
% 2.04/2.21 (b(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[63, 11810])).
% 2.04/2.21 tff(11812,plain,
% 2.04/2.21 (~b(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11807, 3406])).
% 2.04/2.21 tff(11813,plain,
% 2.04/2.21 (r(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[289, 11812])).
% 2.04/2.21 tff(11814,plain,
% 2.04/2.21 (~(elem!1 = s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3980, 340, 11792])).
% 2.04/2.21 tff(11815,plain,
% 2.04/2.21 (r(z, elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11183, 228, 340, 3406, 2247, 11812, 518])).
% 2.04/2.21 tff(11816,plain,
% 2.04/2.21 (~r(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3295, 11815, 11813])).
% 2.04/2.21 tff(11817,plain,
% 2.04/2.21 (s(z) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[357, 11816, 340])).
% 2.04/2.21 tff(11818,plain,
% 2.04/2.21 (s(s(z)) = s(elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11817])).
% 2.04/2.21 tff(11819,plain,
% 2.04/2.21 (s(elem!1) = s(s(z))),
% 2.04/2.21 inference(symmetry,[status(thm)],[11818])).
% 2.04/2.21 tff(11820,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11819])).
% 2.04/2.21 tff(11821,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[11820])).
% 2.04/2.21 tff(11822,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3287, 11815, 228])).
% 2.04/2.21 tff(11823,plain,
% 2.04/2.21 (elem!1 = s(z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1984, 11817])).
% 2.04/2.21 tff(11824,plain,
% 2.04/2.21 (~b(elem!1, z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1992, 11823, 1989])).
% 2.04/2.21 tff(11825,plain,
% 2.04/2.21 (r(elem!1, z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[545, 11824, 534])).
% 2.04/2.21 tff(11826,plain,
% 2.04/2.21 (~r(elem!1, s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2671, 11825, 228])).
% 2.04/2.21 tff(11827,plain,
% 2.04/2.21 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4700, 11199, 340])).
% 2.04/2.21 tff(11828,plain,
% 2.04/2.21 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11817])).
% 2.04/2.21 tff(11829,plain,
% 2.04/2.21 (b(s(s(z)), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11112, 11828])).
% 2.04/2.21 tff(11830,plain,
% 2.04/2.21 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4415, 11829, 11827, 11826, 11822])).
% 2.04/2.21 tff(11831,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[149, 11830])).
% 2.04/2.21 tff(11832,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11831, 11821])).
% 2.04/2.21 tff(11833,plain,
% 2.04/2.21 (s(s(s(z))) = s(s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11818])).
% 2.04/2.21 tff(11834,plain,
% 2.04/2.21 (s(s(elem!1)) = s(s(s(z)))),
% 2.04/2.21 inference(symmetry,[status(thm)],[11833])).
% 2.04/2.21 tff(11835,plain,
% 2.04/2.21 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11834])).
% 2.04/2.21 tff(11836,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.04/2.21 inference(symmetry,[status(thm)],[11835])).
% 2.04/2.21 tff(11837,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11818])).
% 2.04/2.21 tff(11838,plain,
% 2.04/2.21 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11171, 11837])).
% 2.04/2.21 tff(11839,plain,
% 2.04/2.21 (r(s(elem!1), s(s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11838, 11836])).
% 2.04/2.21 tff(11840,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11833])).
% 2.04/2.21 tff(11841,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[3953, 11840])).
% 2.04/2.21 tff(11842,plain,
% 2.04/2.21 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8986, 77, 11841, 11839])).
% 2.04/2.21 tff(11843,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11842, 11832])).
% 2.04/2.21 tff(11844,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), z) | b(s(z), elem!1) | (~b(s(s(s(z))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11845,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11844, 518, 1989, 340, 2247, 3953])).
% 2.04/2.21 tff(11846,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[247, 11845])).
% 2.04/2.21 tff(11847,plain,
% 2.04/2.21 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[576])).
% 2.04/2.21 tff(11848,plain,
% 2.04/2.21 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.04/2.21 inference(symmetry,[status(thm)],[11847])).
% 2.04/2.21 tff(11849,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11850,plain,
% 2.04/2.21 (((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11851,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11850])).
% 2.04/2.21 tff(11852,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[11851, 11849])).
% 2.04/2.21 tff(11853,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(11854,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11853, 11852])).
% 2.04/2.21 tff(11855,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11854, 116, 1055, 212, 7113, 2442, 254])).
% 2.04/2.21 tff(11856,plain,((~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11857,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11856, 254, 1055, 9605])).
% 2.04/2.21 tff(11858,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[226, 11857])).
% 2.04/2.21 tff(11859,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5905, 11858, 3953])).
% 2.04/2.21 tff(11860,plain,
% 2.04/2.21 (~r(s(s(s(z))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9083, 11859, 370])).
% 2.04/2.21 tff(11861,plain,
% 2.04/2.21 (b(s(s(s(z))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2725, 11860, 7622])).
% 2.04/2.21 tff(11862,plain,
% 2.04/2.21 (~b(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5560, 11861, 1055, 7540])).
% 2.04/2.21 tff(11863,plain,
% 2.04/2.21 (r(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[63, 11862])).
% 2.04/2.21 tff(11864,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[370])).
% 2.04/2.21 tff(11865,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11858, 11864])).
% 2.04/2.21 tff(11866,plain,
% 2.04/2.21 (~b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8729, 11865, 11863, 1989, 518, 7540, 3953, 254])).
% 2.04/2.21 tff(11867,plain,
% 2.04/2.21 (r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1345, 11866, 8389])).
% 2.04/2.21 tff(11868,plain,
% 2.04/2.21 (r(elem!1, s(elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11867, 11848])).
% 2.04/2.21 tff(11869,plain,
% 2.04/2.21 (r(s(s(elem!1)), s(elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[3953, 8371])).
% 2.04/2.21 tff(11870,plain,
% 2.04/2.21 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7632, 11857, 370])).
% 2.04/2.21 tff(11871,plain,
% 2.04/2.21 (r(s(s(elem!1)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[743, 11870, 7625])).
% 2.04/2.21 tff(11872,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11873,plain,
% 2.04/2.21 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11874,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11873])).
% 2.04/2.21 tff(11875,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[11874, 11872])).
% 2.04/2.21 tff(11876,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(11877,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11876, 11875])).
% 2.04/2.21 tff(11878,plain,
% 2.04/2.21 (~r(elem!1, s(elem!1))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11877, 77, 11871, 11869])).
% 2.04/2.21 tff(11879,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11878, 11868])).
% 2.04/2.21 tff(11880,plain,((~b(s(s(s(s(z)))), z)) | (~(s(s(z)) = elem!1)) | b(s(z), z) | (z = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11881,plain,
% 2.04/2.21 (~(s(s(z)) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11880, 1055, 1989, 518, 11846, 3953])).
% 2.04/2.21 tff(11882,plain,
% 2.04/2.21 (~(s(z) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4796, 1055, 11812])).
% 2.04/2.21 tff(11883,plain,
% 2.04/2.21 (~b(s(s(z)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8268, 11882, 340, 2247, 1055, 534])).
% 2.04/2.21 tff(11884,plain,
% 2.04/2.21 (r(s(s(z)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[426, 11883, 11881])).
% 2.04/2.21 tff(11885,plain,
% 2.04/2.21 (~r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5025, 11884, 2235])).
% 2.04/2.21 tff(11886,plain,
% 2.04/2.21 (r(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[357, 11882, 340])).
% 2.04/2.21 tff(11887,plain,
% 2.04/2.21 (~r(elem!1, z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2815, 11886, 3406])).
% 2.04/2.21 tff(11888,plain,
% 2.04/2.21 (b(elem!1, z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[545, 11887, 534])).
% 2.04/2.21 tff(11889,plain,
% 2.04/2.21 (~b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5469, 11888, 2247, 1055])).
% 2.04/2.21 tff(11890,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1345, 11889, 11885, 11814])).
% 2.04/2.21 tff(11891,plain,((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | b(s(z), elem!1) | b(s(z), z) | (z = elem!1) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11892,plain,
% 2.04/2.21 (~b(z, elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11891, 2235, 2247, 340, 1989, 518, 3953])).
% 2.04/2.21 tff(11893,plain,
% 2.04/2.21 (r(z, elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1044, 11892, 518])).
% 2.04/2.21 tff(11894,plain,
% 2.04/2.21 (~r(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3295, 11893, 11813])).
% 2.04/2.21 tff(11895,plain,
% 2.04/2.21 (s(z) = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[357, 11894, 340])).
% 2.04/2.21 tff(11896,plain,
% 2.04/2.21 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1531, 11895])).
% 2.04/2.21 tff(11897,plain,
% 2.04/2.21 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1584, 11896])).
% 2.04/2.21 tff(11898,plain,
% 2.04/2.21 (s(s(z)) = s(elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11895])).
% 2.04/2.21 tff(11899,plain,
% 2.04/2.21 (s(s(s(z))) = s(s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11898])).
% 2.04/2.21 tff(11900,plain,
% 2.04/2.21 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11899])).
% 2.04/2.21 tff(11901,plain,
% 2.04/2.21 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11895])).
% 2.04/2.21 tff(11902,plain,
% 2.04/2.21 (b(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11792, 11901])).
% 2.04/2.21 tff(11903,plain,
% 2.04/2.21 (b(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11902, 11900])).
% 2.04/2.21 tff(11904,plain,
% 2.04/2.21 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11898])).
% 2.04/2.21 tff(11905,plain,
% 2.04/2.21 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11895])).
% 2.04/2.21 tff(11906,plain,
% 2.04/2.21 (b(s(s(z)), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11112, 11905])).
% 2.04/2.21 tff(11907,plain,
% 2.04/2.21 (b(s(elem!1), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11906, 11904])).
% 2.04/2.21 tff(11908,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11898])).
% 2.04/2.21 tff(11909,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4986, 11908])).
% 2.04/2.21 tff(11910,plain,
% 2.04/2.21 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11895])).
% 2.04/2.21 tff(11911,plain,
% 2.04/2.21 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11910])).
% 2.04/2.21 tff(11912,plain,
% 2.04/2.21 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[566, 11911])).
% 2.04/2.21 tff(11913,plain,
% 2.04/2.21 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11899])).
% 2.04/2.21 tff(11914,plain,
% 2.04/2.21 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[11913, 1504])).
% 2.04/2.21 tff(11915,plain,
% 2.04/2.21 ((~(s(s(s(s(s(z))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11914])).
% 2.04/2.21 tff(11916,plain,
% 2.04/2.21 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[1138, 11915])).
% 2.04/2.21 tff(11917,plain,
% 2.04/2.21 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11895])).
% 2.04/2.21 tff(11918,plain,
% 2.04/2.21 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.21 inference(transitivity,[status(thm)],[11917, 4222])).
% 2.04/2.21 tff(11919,plain,
% 2.04/2.21 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11918])).
% 2.04/2.21 tff(11920,plain,
% 2.04/2.21 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[1901, 11919])).
% 2.04/2.21 tff(11921,plain,
% 2.04/2.21 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11899])).
% 2.04/2.21 tff(11922,plain,
% 2.04/2.21 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[5017, 11921])).
% 2.04/2.21 tff(11923,plain,
% 2.04/2.21 (b(s(s(elem!1)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2832, 11895, 2247])).
% 2.04/2.21 tff(11924,assumption,(b(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.21 tff(11925,plain,
% 2.04/2.21 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1033, 9498, 448, 573, 752, 953])).
% 2.04/2.21 tff(11926,plain,
% 2.04/2.21 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[885, 11925, 952])).
% 2.04/2.21 tff(11927,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11928,plain,
% 2.04/2.21 (((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(11929,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11928])).
% 2.04/2.21 tff(11930,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[11929, 11927])).
% 2.04/2.21 tff(11931,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(11932,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[11931, 11930])).
% 2.04/2.21 tff(11933,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11932, 116, 9498, 1879, 573, 11926, 11924])).
% 2.04/2.21 tff(11934,plain,((~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (s(s(s(s(s(z))))) = elem!1) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(11935,plain,
% 2.04/2.21 (~r(s(s(elem!1)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[11934, 11903, 11923, 11922, 11920, 11893, 11916])).
% 2.04/2.21 tff(11936,plain,
% 2.04/2.21 (b(s(s(elem!1)), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[743, 11935, 11912])).
% 2.04/2.21 tff(11937,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[10638, 11936, 11909, 11907, 11903])).
% 2.04/2.21 tff(11938,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1596, 11937, 11897])).
% 2.04/2.21 tff(11939,plain,
% 2.04/2.21 (~r(z, s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3088, 77, 11893, 11938])).
% 2.04/2.21 tff(11940,plain,
% 2.04/2.21 (b(z, s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1576, 21, 11939, 1563])).
% 2.04/2.21 tff(11941,plain,
% 2.04/2.21 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11898])).
% 2.04/2.21 tff(11942,plain,
% 2.04/2.21 (b(s(elem!1), z)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7113, 11941])).
% 2.04/2.21 tff(11943,plain,
% 2.04/2.21 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[11898])).
% 2.04/2.21 tff(11944,plain,
% 2.04/2.21 (b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[5008, 11943])).
% 2.04/2.21 tff(11945,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(11946,plain,
% 2.04/2.22 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(11947,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11946])).
% 2.04/2.22 tff(11948,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[11947, 11945])).
% 2.04/2.22 tff(11949,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(11950,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[11949, 11948])).
% 2.04/2.22 tff(11951,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11950, 116, 11907, 11909, 11944, 11942, 11940])).
% 2.04/2.22 tff(11952,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(s(z), elem!1) | (z = elem!1) | b(s(z), z) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(11953,plain,
% 2.04/2.22 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11952, 518, 340, 2247, 1989, 3953])).
% 2.04/2.22 tff(11954,plain,
% 2.04/2.22 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[105, 11953])).
% 2.04/2.22 tff(11955,plain,
% 2.04/2.22 (~b(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11132, 11954, 2247])).
% 2.04/2.22 tff(11956,plain,
% 2.04/2.22 (r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1174, 11955])).
% 2.04/2.22 tff(11957,plain,
% 2.04/2.22 (~r(s(z), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[10272, 11956, 3406])).
% 2.04/2.22 tff(11958,plain,
% 2.04/2.22 (b(s(z), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[172, 11957])).
% 2.04/2.22 tff(11959,plain,
% 2.04/2.22 (~(s(s(z)) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[376, 11958, 340])).
% 2.04/2.22 tff(11960,plain,
% 2.04/2.22 (~(s(z) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4796, 1055, 11808])).
% 2.04/2.22 tff(11961,plain,
% 2.04/2.22 (r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[357, 11960, 340])).
% 2.04/2.22 tff(11962,plain,
% 2.04/2.22 (~b(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8268, 11960, 340, 2247, 1055, 439])).
% 2.04/2.22 tff(11963,plain,
% 2.04/2.22 (r(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[426, 11962, 422])).
% 2.04/2.22 tff(11964,plain,
% 2.04/2.22 (~r(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5490, 11963, 11961, 2247, 1055])).
% 2.04/2.22 tff(11965,plain,
% 2.04/2.22 (~r(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2815, 11961, 155])).
% 2.04/2.22 tff(11966,plain,
% 2.04/2.22 (b(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[545, 11965, 439])).
% 2.04/2.22 tff(11967,plain,
% 2.04/2.22 (~b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5469, 11966, 2247, 1055])).
% 2.04/2.22 tff(11968,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1345, 11967, 11964, 11814])).
% 2.04/2.22 tff(11969,plain,((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (elem!1 = z) | (s(s(z)) = elem!1) | (~r(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(11970,plain,
% 2.04/2.22 (~b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11969, 534, 2247, 11959, 3406, 340])).
% 2.04/2.22 tff(11971,plain,
% 2.04/2.22 (r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1044, 11970, 518])).
% 2.04/2.22 tff(11972,plain,
% 2.04/2.22 (~r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3295, 11971, 11813])).
% 2.04/2.22 tff(11973,plain,
% 2.04/2.22 (s(z) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[357, 11972, 340])).
% 2.04/2.22 tff(11974,plain,
% 2.04/2.22 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11973])).
% 2.04/2.22 tff(11975,plain,
% 2.04/2.22 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11974])).
% 2.04/2.22 tff(11976,plain,
% 2.04/2.22 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[566, 11975])).
% 2.04/2.22 tff(11977,plain,
% 2.04/2.22 (b(s(s(elem!1)), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2832, 11973, 2247])).
% 2.04/2.22 tff(11978,plain,
% 2.04/2.22 (~r(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[10758, 11971, 11956])).
% 2.04/2.22 tff(11979,plain,
% 2.04/2.22 (b(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[426, 11978, 11959])).
% 2.04/2.22 tff(11980,plain,
% 2.04/2.22 (b(s(elem!1), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1549, 11979, 11973])).
% 2.04/2.22 tff(11981,plain,
% 2.04/2.22 (s(s(z)) = s(elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11973])).
% 2.04/2.22 tff(11982,plain,
% 2.04/2.22 (s(s(s(z))) = s(s(elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11981])).
% 2.04/2.22 tff(11983,plain,
% 2.04/2.22 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11982])).
% 2.04/2.22 tff(11984,plain,
% 2.04/2.22 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11973])).
% 2.04/2.22 tff(11985,plain,
% 2.04/2.22 (b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[11792, 11984])).
% 2.04/2.22 tff(11986,plain,
% 2.04/2.22 (b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[11985, 11983])).
% 2.04/2.22 tff(11987,plain,
% 2.04/2.22 (s(s(elem!1)) = s(s(s(z)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[11982])).
% 2.04/2.22 tff(11988,plain,
% 2.04/2.22 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11987])).
% 2.04/2.22 tff(11989,plain,
% 2.04/2.22 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[11988])).
% 2.04/2.22 tff(11990,plain,
% 2.04/2.22 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11981])).
% 2.04/2.22 tff(11991,plain,
% 2.04/2.22 (b(s(elem!1), s(s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[11954, 11990])).
% 2.04/2.22 tff(11992,plain,
% 2.04/2.22 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[11991, 11989])).
% 2.04/2.22 tff(11993,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5293, 11992, 11986, 11971, 11980, 11977, 11976])).
% 2.04/2.22 tff(11994,plain,((z = elem!1) | (~b(s(s(s(z))), z)) | b(s(z), elem!1) | b(s(z), z) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(11995,plain,
% 2.04/2.22 (z = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11994, 3953, 340, 1989, 11811])).
% 2.04/2.22 tff(11996,plain,
% 2.04/2.22 (s(z) = s(elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11995])).
% 2.04/2.22 tff(11997,plain,
% 2.04/2.22 (s(s(z)) = s(s(elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11996])).
% 2.04/2.22 tff(11998,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11997])).
% 2.04/2.22 tff(11999,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11995])).
% 2.04/2.22 tff(12000,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[11999, 1580])).
% 2.04/2.22 tff(12001,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12000])).
% 2.04/2.22 tff(12002,plain,
% 2.04/2.22 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[242, 12001])).
% 2.04/2.22 tff(12003,plain,
% 2.04/2.22 (elem!1 = z),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[445, 11995])).
% 2.04/2.22 tff(12004,plain,
% 2.04/2.22 (b(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7117, 12003])).
% 2.04/2.22 tff(12005,plain,
% 2.04/2.22 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[11995])).
% 2.04/2.22 tff(12006,plain,
% 2.04/2.22 ((~r(s(s(s(z))), z)) <=> (~r(s(s(s(z))), elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12005])).
% 2.04/2.22 tff(12007,plain,
% 2.04/2.22 (~r(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[11810, 12006])).
% 2.04/2.22 tff(12008,plain,
% 2.04/2.22 (~b(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11132, 27, 2247])).
% 2.04/2.22 tff(12009,plain,
% 2.04/2.22 (r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1174, 12008])).
% 2.04/2.22 tff(12010,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11167, 12009, 155])).
% 2.04/2.22 tff(12011,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2421, 12010, 1713])).
% 2.04/2.22 tff(12012,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1596, 12011, 3578])).
% 2.04/2.22 tff(12013,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[10127, 116, 616, 3561, 1054, 1725, 3562])).
% 2.04/2.22 tff(12014,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12015,plain,
% 2.04/2.22 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12014, 12012, 9926, 11610, 8076])).
% 2.04/2.22 tff(12016,plain,
% 2.04/2.22 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1068, 12015, 1718])).
% 2.04/2.22 tff(12017,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4401, 77, 429, 3953, 359])).
% 2.04/2.22 tff(12018,plain,((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12019,plain,
% 2.04/2.22 (~r(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12018, 12016, 3953])).
% 2.04/2.22 tff(12020,plain,
% 2.04/2.22 (b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1345, 12019, 1620])).
% 2.04/2.22 tff(12021,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8092, 116, 11610, 9926, 12020, 8076])).
% 2.04/2.22 tff(12022,plain,((~b(s(s(z)), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(z = elem!1)) | (~r(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12023,plain,
% 2.04/2.22 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12022, 3953, 11814, 11995, 3406, 11811])).
% 2.04/2.22 tff(12024,plain,
% 2.04/2.22 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[105, 12023])).
% 2.04/2.22 tff(12025,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)],[5016, 12024, 3953])).
% 2.04/2.22 tff(12026,plain,
% 2.04/2.22 (~b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5059, 12025, 11792, 11995, 3406, 12007])).
% 2.04/2.22 tff(12027,plain,
% 2.04/2.22 (r(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1345, 12026, 11814])).
% 2.04/2.22 tff(12028,plain,
% 2.04/2.22 (~r(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12018, 12027, 3953])).
% 2.04/2.22 tff(12029,plain,
% 2.04/2.22 (r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2488, 12027, 12003])).
% 2.04/2.22 tff(12030,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5649, 12029, 3953])).
% 2.04/2.22 tff(12031,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2421, 12030, 12003])).
% 2.04/2.22 tff(12032,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[10774, 12031, 12028, 12004, 12002])).
% 2.04/2.22 tff(12033,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[226, 12032])).
% 2.04/2.22 tff(12034,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[12033, 11998])).
% 2.04/2.22 tff(12035,plain,
% 2.04/2.22 (r(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2605, 12024, 11995])).
% 2.04/2.22 tff(12036,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9781, 12035, 3953])).
% 2.04/2.22 tff(12037,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12036, 12034])).
% 2.04/2.22 tff(12038,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(z))), z) | b(s(z), elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12039,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12038, 11810, 340, 1989])).
% 2.04/2.22 tff(12040,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3951, 12039])).
% 2.04/2.22 tff(12041,plain,
% 2.04/2.22 (~(s(s(z)) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[376, 10274, 340])).
% 2.04/2.22 tff(12042,plain,
% 2.04/2.22 (r(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[426, 12041, 1])).
% 2.04/2.22 tff(12043,plain,
% 2.04/2.22 (~b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11969, 12041, 2247, 534, 155, 340])).
% 2.04/2.22 tff(12044,plain,
% 2.04/2.22 (r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1044, 12043, 518])).
% 2.04/2.22 tff(12045,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[10758, 12044, 12042, 1212])).
% 2.04/2.22 tff(12046,plain,((~r(z, s(s(z)))) | (z = elem!1) | b(s(s(z)), elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12047,plain,
% 2.04/2.22 (~r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12046, 1, 518, 2247, 155, 340])).
% 2.04/2.22 tff(12048,plain,
% 2.04/2.22 (b(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1174, 12047])).
% 2.04/2.22 tff(12049,plain,
% 2.04/2.22 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2801, 116, 2247, 28, 12048, 11792])).
% 2.04/2.22 tff(12050,plain,
% 2.04/2.22 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[325, 12049])).
% 2.04/2.22 tff(12051,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8864, 12050, 155])).
% 2.04/2.22 tff(12052,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[247, 12051])).
% 2.04/2.22 tff(12053,plain,
% 2.04/2.22 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2450, 12052, 2247, 28, 12048])).
% 2.04/2.22 tff(12054,plain,
% 2.04/2.22 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[149, 12053])).
% 2.04/2.22 tff(12055,plain,
% 2.04/2.22 (~r(s(z), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[336, 12054, 12050])).
% 2.04/2.22 tff(12056,plain,
% 2.04/2.22 (b(s(z), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[172, 12055])).
% 2.04/2.22 tff(12057,plain,
% 2.04/2.22 (~(s(s(z)) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[376, 12056, 340])).
% 2.04/2.22 tff(12058,plain,
% 2.04/2.22 (~b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11969, 12057, 2247, 534, 155, 340])).
% 2.04/2.22 tff(12059,plain,
% 2.04/2.22 (r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1044, 12058, 518])).
% 2.04/2.22 tff(12060,plain,
% 2.04/2.22 (~r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3295, 12059, 11809])).
% 2.04/2.22 tff(12061,plain,
% 2.04/2.22 (s(z) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[357, 12060, 340])).
% 2.04/2.22 tff(12062,plain,
% 2.04/2.22 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12061])).
% 2.04/2.22 tff(12063,plain,
% 2.04/2.22 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.04/2.22 inference(symmetry,[status(thm)],[12062])).
% 2.04/2.22 tff(12064,plain,
% 2.04/2.22 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(z)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12063])).
% 2.04/2.22 tff(12065,plain,
% 2.04/2.22 (~b(s(s(z)), s(z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1, 12064])).
% 2.04/2.22 tff(12066,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11112, 12065])).
% 2.04/2.22 tff(12067,plain,(b(s(s(z)), elem!1) | b(s(z), elem!1) | (z = elem!1) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12068,plain,
% 2.04/2.22 (b(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12067, 518, 340, 2247, 3406, 28])).
% 2.04/2.22 tff(12069,plain,
% 2.04/2.22 (~(s(z) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4796, 1055, 4794])).
% 2.04/2.22 tff(12070,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8268, 12069, 1055, 340, 2247, 1331, 439])).
% 2.04/2.22 tff(12071,plain,((~b(z, elem!1)) | b(s(z), elem!1) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), elem!1)) | (elem!1 = z) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12072,plain,
% 2.04/2.22 (~b(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12071, 12068, 2247, 340, 534, 11812])).
% 2.04/2.22 tff(12073,plain,
% 2.04/2.22 (r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1044, 12072, 518])).
% 2.04/2.22 tff(12074,plain,
% 2.04/2.22 (~r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3295, 12073, 11813])).
% 2.04/2.22 tff(12075,plain,
% 2.04/2.22 (s(z) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[357, 12074, 340])).
% 2.04/2.22 tff(12076,plain,
% 2.04/2.22 (s(s(z)) = s(elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12075])).
% 2.04/2.22 tff(12077,plain,
% 2.04/2.22 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12076])).
% 2.04/2.22 tff(12078,plain,
% 2.04/2.22 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[12077])).
% 2.04/2.22 tff(12079,plain,
% 2.04/2.22 ((~b(z, s(elem!1))) <=> (~b(z, s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12078])).
% 2.04/2.22 tff(12080,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2016, 12075, 28])).
% 2.04/2.22 tff(12081,plain,
% 2.04/2.22 (b(s(s(elem!1)), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2832, 12075, 2247])).
% 2.04/2.22 tff(12082,plain,
% 2.04/2.22 (s(s(s(z))) = s(s(elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12076])).
% 2.04/2.22 tff(12083,plain,
% 2.04/2.22 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12082])).
% 2.04/2.22 tff(12084,plain,
% 2.04/2.22 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12075])).
% 2.04/2.22 tff(12085,plain,
% 2.04/2.22 (b(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[11792, 12084])).
% 2.04/2.22 tff(12086,plain,
% 2.04/2.22 (b(elem!1, s(s(elem!1)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[12085, 12083])).
% 2.04/2.22 tff(12087,plain,
% 2.04/2.22 (elem!1 = s(z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1984, 12075])).
% 2.04/2.22 tff(12088,plain,
% 2.04/2.22 (~b(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1992, 12087, 1989])).
% 2.04/2.22 tff(12089,plain,
% 2.04/2.22 (r(elem!1, z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[545, 12088, 534])).
% 2.04/2.22 tff(12090,plain,
% 2.04/2.22 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1531, 12075])).
% 2.04/2.22 tff(12091,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(12092,plain,
% 2.04/2.22 (((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(12093,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12092])).
% 2.04/2.22 tff(12094,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[12093, 12091])).
% 2.04/2.22 tff(12095,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(12096,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[12095, 12094])).
% 2.04/2.22 tff(12097,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12096, 116, 1879, 573, 2023, 8835])).
% 2.04/2.22 tff(12098,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(12099,plain,
% 2.04/2.22 (((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(12100,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12099])).
% 2.04/2.22 tff(12101,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[12100, 12098])).
% 2.04/2.22 tff(12102,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(12103,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[12102, 12101])).
% 2.04/2.22 tff(12104,plain,
% 2.04/2.22 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12103, 116, 1879, 573, 2023, 8835])).
% 2.04/2.22 tff(12105,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3103, 12104, 12097, 2247, 28, 448, 1362, 575])).
% 2.04/2.22 tff(12106,plain,((~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12107,plain,
% 2.04/2.22 (~b(z, s(elem!1))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12106, 12073, 28, 2247, 12090, 12089, 12086, 12081, 12080])).
% 2.04/2.22 tff(12108,plain,
% 2.04/2.22 (~b(z, s(s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[12107, 12079])).
% 2.04/2.22 tff(12109,plain,
% 2.04/2.22 (r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1174, 12108])).
% 2.04/2.22 tff(12110,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11167, 12109, 3406])).
% 2.04/2.22 tff(12111,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[247, 12110])).
% 2.04/2.22 tff(12112,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3390, 27, 2247, 340, 11809, 28, 1331, 448])).
% 2.04/2.22 tff(12113,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[247, 12112])).
% 2.04/2.22 tff(12114,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11167, 12113, 12009, 155])).
% 2.04/2.22 tff(12115,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(s(z))), z)) | b(s(z), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12116,plain,
% 2.04/2.22 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12115, 12068, 2247, 340, 28, 3406, 12073])).
% 2.04/2.22 tff(12117,plain,
% 2.04/2.22 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[105, 12116])).
% 2.04/2.22 tff(12118,plain,
% 2.04/2.22 (~r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9352, 12109, 12117])).
% 2.04/2.22 tff(12119,plain,
% 2.04/2.22 (b(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11399, 12118])).
% 2.04/2.22 tff(12120,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2255, 12119, 12111, 2247, 28])).
% 2.04/2.22 tff(12121,plain,((z = elem!1) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(z), elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(12122,plain,
% 2.04/2.22 (z = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[12121, 11811, 12040, 340, 1989])).
% 2.04/2.22 tff(12123,plain,
% 2.04/2.22 (s(z) = s(elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12122])).
% 2.04/2.22 tff(12124,plain,
% 2.04/2.22 (s(s(z)) = s(s(elem!1))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12123])).
% 2.04/2.22 tff(12125,plain,
% 2.04/2.22 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12124])).
% 2.04/2.22 tff(12126,plain,
% 2.04/2.22 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[10042, 12122, 11811, 340, 12040])).
% 2.04/2.22 tff(12127,plain,
% 2.04/2.22 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[105, 12126])).
% 2.04/2.22 tff(12128,plain,
% 2.04/2.22 (b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[12127, 12125])).
% 2.04/2.22 tff(12129,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12122])).
% 2.04/2.22 tff(12130,plain,
% 2.04/2.22 (~b(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11132, 12127, 11811])).
% 2.04/2.22 tff(12131,plain,
% 2.04/2.22 (r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1174, 12130])).
% 2.04/2.22 tff(12132,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11167, 12131, 3406])).
% 2.04/2.22 tff(12133,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[247, 12132])).
% 2.04/2.22 tff(12134,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[12133, 12129])).
% 2.04/2.22 tff(12135,plain,
% 2.04/2.22 (~b(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2255, 12133, 11811, 12040])).
% 2.04/2.22 tff(12136,plain,
% 2.04/2.22 (r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[11399, 12135])).
% 2.04/2.22 tff(12137,plain,
% 2.04/2.22 (elem!1 = z),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[445, 12122])).
% 2.04/2.22 tff(12138,plain,
% 2.04/2.22 (~b(z, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3100, 12133, 11811, 12040])).
% 2.04/2.22 tff(12139,plain,
% 2.04/2.22 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3626, 12138, 12122])).
% 2.04/2.22 tff(12140,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12122])).
% 2.04/2.22 tff(12141,plain,
% 2.04/2.22 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[12140, 1580])).
% 2.04/2.22 tff(12142,plain,
% 2.04/2.22 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12141])).
% 2.04/2.22 tff(12143,plain,
% 2.04/2.22 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[242, 12142])).
% 2.04/2.22 tff(12144,plain,
% 2.04/2.22 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1068, 12143, 12139])).
% 2.04/2.22 tff(12145,plain,
% 2.04/2.22 (r(z, s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2440, 12144, 12137])).
% 2.04/2.22 tff(12146,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2461, 12145, 12136])).
% 2.04/2.22 tff(12147,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1146, 12146])).
% 2.04/2.22 tff(12148,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1572, 12145, 12131])).
% 2.04/2.22 tff(12149,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[226, 12148])).
% 2.04/2.22 tff(12150,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3559, 12149, 12137])).
% 2.04/2.22 tff(12151,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(12152,plain,
% 2.04/2.22 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(12153,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[12152])).
% 2.04/2.22 tff(12154,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[12153, 12151])).
% 2.04/2.22 tff(12155,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(12156,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12155, 12154])).
% 2.04/2.23 tff(12157,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12156, 116, 12040, 12150, 12147, 12134, 12128])).
% 2.04/2.23 tff(12158,plain,(r(s(s(s(z))), z) | b(s(z), elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12159,plain,
% 2.04/2.23 (r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12158, 1989, 340])).
% 2.04/2.23 tff(12160,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2136, 12159, 3406])).
% 2.04/2.23 tff(12161,plain,
% 2.04/2.23 (b(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[402, 21, 135, 12160])).
% 2.04/2.23 tff(12162,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12163,plain,
% 2.04/2.23 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12164,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12163])).
% 2.04/2.23 tff(12165,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[12164, 12162])).
% 2.04/2.23 tff(12166,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(12167,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12166, 12165])).
% 2.04/2.23 tff(12168,plain,
% 2.04/2.23 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12167, 116, 11792, 11112, 12161])).
% 2.04/2.23 tff(12169,plain,
% 2.04/2.23 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[105, 12168])).
% 2.04/2.23 tff(12170,plain,
% 2.04/2.23 ((~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8970, 7113])).
% 2.04/2.23 tff(12171,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12170, 12169, 11792, 3406, 12159, 11813])).
% 2.04/2.23 tff(12172,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3951, 12171])).
% 2.04/2.23 tff(12173,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3961, 12172, 12159])).
% 2.04/2.23 tff(12174,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[247, 12173])).
% 2.04/2.23 tff(12175,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12176,plain,
% 2.04/2.23 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12177,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12176])).
% 2.04/2.23 tff(12178,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[12177, 12175])).
% 2.04/2.23 tff(12179,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(12180,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12179, 12178])).
% 2.04/2.23 tff(12181,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12180, 116, 11792, 11112, 12161])).
% 2.04/2.23 tff(12182,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[89, 21, 12181, 56])).
% 2.04/2.23 tff(12183,plain,
% 2.04/2.23 (~r(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7618, 12182, 12159])).
% 2.04/2.23 tff(12184,plain,
% 2.04/2.23 (b(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1174, 12183])).
% 2.04/2.23 tff(12185,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4984, 77, 12169, 12172])).
% 2.04/2.23 tff(12186,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[226, 12185])).
% 2.04/2.23 tff(12187,plain,
% 2.04/2.23 (((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12188,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12187])).
% 2.04/2.23 tff(12189,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[12188, 10353])).
% 2.04/2.23 tff(12190,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(12191,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12190, 12189])).
% 2.04/2.23 tff(12192,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12191, 116, 12186, 7113, 12184, 12174])).
% 2.04/2.23 tff(12193,plain,(b(s(z), z) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12194,plain,
% 2.04/2.23 (b(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12193, 340])).
% 2.04/2.23 tff(12195,plain,
% 2.04/2.23 (((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12196,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12195])).
% 2.04/2.23 tff(12197,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[12196, 2693])).
% 2.04/2.23 tff(12198,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(12199,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12198, 12197])).
% 2.04/2.23 tff(12200,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12199, 116, 270, 271, 7113, 11112])).
% 2.04/2.23 tff(12201,plain,((~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12202,plain,
% 2.04/2.23 (~b(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12201, 12194])).
% 2.04/2.23 tff(12203,plain,
% 2.04/2.23 (r(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[289, 12202])).
% 2.04/2.23 tff(12204,plain,
% 2.04/2.23 (~(elem!1 = z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[409, 12194, 340])).
% 2.04/2.23 tff(12205,plain,
% 2.04/2.23 (~(z = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[445, 12204])).
% 2.04/2.23 tff(12206,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12207,plain,
% 2.04/2.23 (((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(12208,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12207])).
% 2.04/2.23 tff(12209,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[12208, 12206])).
% 2.04/2.23 tff(12210,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(12211,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12210, 12209])).
% 2.04/2.23 tff(12212,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12211, 116, 270, 7113, 2442, 11112])).
% 2.04/2.23 tff(12213,plain,((~b(z, s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12214,plain,
% 2.04/2.23 (~b(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12213, 12194])).
% 2.04/2.23 tff(12215,plain,
% 2.04/2.23 (r(z, s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1174, 12214])).
% 2.04/2.23 tff(12216,plain,
% 2.04/2.23 (~r(s(s(z)), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[10758, 448, 12215])).
% 2.04/2.23 tff(12217,plain,
% 2.04/2.23 (s(s(z)) = elem!1),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[426, 12216, 1])).
% 2.04/2.23 tff(12218,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[480, 12217, 4748])).
% 2.04/2.23 tff(12219,plain,((~r(z, elem!1)) | b(s(s(z)), elem!1) | b(s(z), elem!1) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12220,plain,
% 2.04/2.23 (~r(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12219, 9390, 340, 1])).
% 2.04/2.23 tff(12221,plain,
% 2.04/2.23 (b(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1044, 12220, 12205])).
% 2.04/2.23 tff(12222,plain,
% 2.04/2.23 (~b(elem!1, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[11428, 12221, 12194])).
% 2.04/2.23 tff(12223,plain,
% 2.04/2.23 (~(s(z) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4796, 12221, 4794])).
% 2.04/2.23 tff(12224,plain,
% 2.04/2.23 (~(elem!1 = s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[420, 12223])).
% 2.04/2.23 tff(12225,plain,
% 2.04/2.23 (r(elem!1, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[633, 12224, 12222])).
% 2.04/2.23 tff(12226,plain,
% 2.04/2.23 (~r(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2095, 12225, 9390])).
% 2.04/2.23 tff(12227,plain,
% 2.04/2.23 (b(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[545, 12226, 12204])).
% 2.04/2.23 tff(12228,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9409, 116, 12221, 12227, 12194, 7113, 11112])).
% 2.04/2.23 tff(12229,plain,(b(z, s(z)) | b(s(z), elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12230,plain,
% 2.04/2.23 (b(s(s(z)), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12229, 12202, 340])).
% 2.04/2.23 tff(12231,plain,
% 2.04/2.23 ((~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(s(z))) = elem!1) | (elem!1 = s(s(s(z)))) | (~r(elem!1, z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2734, 7113])).
% 2.04/2.23 tff(12232,plain,
% 2.04/2.23 (~r(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12231, 1055, 11310, 1331, 67, 1620])).
% 2.04/2.23 tff(12233,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[545, 12232, 8263, 439])).
% 2.04/2.23 tff(12234,plain,((~b(z, elem!1)) | (elem!1 = z) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(z))), z)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12235,plain,
% 2.04/2.23 (~b(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12234, 67, 12230, 12204, 11814])).
% 2.04/2.23 tff(12236,plain,
% 2.04/2.23 (r(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1044, 12235, 12205])).
% 2.04/2.23 tff(12237,plain,
% 2.04/2.23 (~r(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3295, 12236, 12203])).
% 2.04/2.23 tff(12238,plain,
% 2.04/2.23 (s(z) = elem!1),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[357, 12237, 340])).
% 2.04/2.23 tff(12239,plain,
% 2.04/2.23 (s(s(z)) = s(elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12238])).
% 2.04/2.23 tff(12240,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12239])).
% 2.04/2.23 tff(12241,plain,
% 2.04/2.23 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12238])).
% 2.04/2.23 tff(12242,plain,
% 2.04/2.23 (b(elem!1, s(s(s(z))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[11792, 12241])).
% 2.04/2.23 tff(12243,plain,
% 2.04/2.23 (b(elem!1, z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1458, 12238, 12194])).
% 2.04/2.23 tff(12244,plain,
% 2.04/2.23 (~(s(s(s(z))) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[11309, 11814])).
% 2.04/2.23 tff(12245,plain,
% 2.04/2.23 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12238])).
% 2.04/2.23 tff(12246,plain,
% 2.04/2.23 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(z))), elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12245])).
% 2.04/2.23 tff(12247,plain,
% 2.04/2.23 (~r(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[10803, 12236, 67, 12203])).
% 2.04/2.23 tff(12248,plain,
% 2.04/2.23 (~r(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12247, 12246])).
% 2.04/2.23 tff(12249,plain,
% 2.04/2.23 (b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2725, 12248, 12244])).
% 2.04/2.23 tff(12250,plain,
% 2.04/2.23 (~b(z, s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9532, 12249, 12243, 12242])).
% 2.04/2.23 tff(12251,plain,
% 2.04/2.23 (r(z, s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[11399, 12250])).
% 2.04/2.23 tff(12252,plain,
% 2.04/2.23 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9352, 12251, 12215])).
% 2.04/2.23 tff(12253,plain,
% 2.04/2.23 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[105, 12252])).
% 2.04/2.23 tff(12254,plain,
% 2.04/2.23 (b(s(elem!1), s(s(s(z))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12253, 12240])).
% 2.04/2.23 tff(12255,plain,
% 2.04/2.23 (b(s(elem!1), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1549, 12238, 12230])).
% 2.04/2.23 tff(12256,plain,
% 2.04/2.23 (~b(s(elem!1), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6850, 12249, 12255, 12242])).
% 2.04/2.23 tff(12257,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12256, 12254])).
% 2.04/2.23 tff(12258,plain,((~r(s(s(s(z))), z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(12259,plain,
% 2.04/2.23 (~r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12258, 340])).
% 2.04/2.23 tff(12260,plain,
% 2.04/2.23 (b(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[63, 12259])).
% 2.04/2.23 tff(12261,plain,
% 2.04/2.23 (~b(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[12071, 12260, 12204, 340, 12230, 12202])).
% 2.04/2.23 tff(12262,plain,
% 2.04/2.23 (r(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1044, 12261, 12205])).
% 2.04/2.23 tff(12263,plain,
% 2.04/2.23 (~r(s(z), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3295, 12262, 12203])).
% 2.04/2.23 tff(12264,plain,
% 2.04/2.23 (s(z) = elem!1),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[357, 12263, 340])).
% 2.04/2.23 tff(12265,plain,
% 2.04/2.23 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1531, 12264])).
% 2.04/2.23 tff(12266,plain,
% 2.04/2.23 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1364, 12265])).
% 2.04/2.23 tff(12267,plain,
% 2.04/2.23 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12266, 4213])).
% 2.04/2.23 tff(12268,plain,
% 2.04/2.23 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12264])).
% 2.04/2.23 tff(12269,plain,
% 2.04/2.23 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.23 inference(transitivity,[status(thm)],[12268, 4222])).
% 2.04/2.23 tff(12270,plain,
% 2.04/2.23 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12269])).
% 2.04/2.23 tff(12271,plain,
% 2.04/2.23 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[1901, 12270])).
% 2.04/2.23 tff(12272,plain,
% 2.04/2.23 ((s(elem!1) = s(z)) <=> (s(elem!1) = elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12264])).
% 2.04/2.23 tff(12273,plain,
% 2.04/2.23 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(z))),
% 2.04/2.23 inference(symmetry,[status(thm)],[12272])).
% 2.04/2.23 tff(12274,plain,
% 2.04/2.23 (s(s(z)) = s(elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12264])).
% 2.04/2.23 tff(12275,plain,
% 2.04/2.23 (s(elem!1) = s(s(z))),
% 2.04/2.23 inference(symmetry,[status(thm)],[12274])).
% 2.04/2.23 tff(12276,plain,
% 2.04/2.23 ((s(elem!1) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12275])).
% 2.04/2.23 tff(12277,plain,
% 2.04/2.23 ((s(s(z)) = elem!1) <=> (s(elem!1) = elem!1)),
% 2.04/2.23 inference(symmetry,[status(thm)],[12276])).
% 2.04/2.23 tff(12278,plain,
% 2.04/2.23 ((s(s(z)) = elem!1) <=> (s(elem!1) = s(z))),
% 2.04/2.23 inference(transitivity,[status(thm)],[12277, 12273])).
% 2.04/2.23 tff(12279,plain,
% 2.04/2.23 ((~(s(s(z)) = elem!1)) <=> (~(s(elem!1) = s(z)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12278])).
% 2.04/2.23 tff(12280,plain,
% 2.04/2.23 (~(s(s(z)) = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[480, 12264])).
% 2.04/2.23 tff(12281,plain,
% 2.04/2.23 (~(s(elem!1) = s(z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12280, 12279])).
% 2.04/2.23 tff(12282,plain,
% 2.04/2.23 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12274])).
% 2.04/2.23 tff(12283,plain,
% 2.04/2.23 (b(s(elem!1), z)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[7113, 12282])).
% 2.04/2.23 tff(12284,plain,
% 2.04/2.23 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6919, 12283, 12194, 12262, 12266, 12281])).
% 2.04/2.23 tff(12285,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[885, 12284, 12271])).
% 2.04/2.23 tff(12286,plain,
% 2.04/2.23 (b(s(s(elem!1)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2832, 12264, 12260])).
% 2.04/2.23 tff(12287,plain,
% 2.04/2.23 (b(s(elem!1), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1549, 12264, 12230])).
% 2.04/2.23 tff(12288,plain,
% 2.04/2.23 (s(s(s(z))) = s(s(elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12274])).
% 2.04/2.23 tff(12289,plain,
% 2.04/2.23 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12288])).
% 2.04/2.23 tff(12290,plain,
% 2.04/2.23 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[12264])).
% 2.04/2.23 tff(12291,plain,
% 2.04/2.23 (b(elem!1, s(s(s(z))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[11792, 12290])).
% 2.04/2.23 tff(12292,plain,
% 2.04/2.23 (b(elem!1, s(s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[12291, 12289])).
% 2.04/2.23 tff(12293,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12294,plain,
% 2.04/2.24 (((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12295,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12294])).
% 2.04/2.24 tff(12296,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[12295, 12293])).
% 2.04/2.24 tff(12297,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(12298,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12297, 12296])).
% 2.04/2.24 tff(12299,plain,
% 2.04/2.24 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12298, 116, 12292, 12287, 12286, 12285])).
% 2.04/2.24 tff(12300,plain,
% 2.04/2.24 ((s(s(s(s(s(z))))) = s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4324, 21, 12299])).
% 2.04/2.24 tff(12301,plain,
% 2.04/2.24 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12300, 12267])).
% 2.04/2.24 tff(12302,plain,
% 2.04/2.24 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12274])).
% 2.04/2.24 tff(12303,plain,
% 2.04/2.24 (r(z, s(elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12215, 12302])).
% 2.04/2.24 tff(12304,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12305,plain,
% 2.04/2.24 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12306,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12305])).
% 2.04/2.24 tff(12307,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[12306, 12304])).
% 2.04/2.24 tff(12308,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(12309,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12308, 12307])).
% 2.04/2.24 tff(12310,plain,
% 2.04/2.24 (~r(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12309, 77, 12303, 12301])).
% 2.04/2.24 tff(12311,plain,
% 2.04/2.24 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3778, 21, 12310])).
% 2.04/2.24 tff(12312,plain,
% 2.04/2.24 (b(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12311, 3768])).
% 2.04/2.24 tff(12313,plain,
% 2.04/2.24 (b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1458, 12264, 12194])).
% 2.04/2.24 tff(12314,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12315,plain,
% 2.04/2.24 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12316,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12315])).
% 2.04/2.24 tff(12317,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[12316, 12314])).
% 2.04/2.24 tff(12318,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(12319,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12318, 12317])).
% 2.04/2.24 tff(12320,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12319, 116, 12313, 12287, 12283, 12285, 12312])).
% 2.04/2.24 tff(12321,plain,(b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12322,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[10264, 67, 12321, 155])).
% 2.04/2.24 tff(12323,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[247, 12322])).
% 2.04/2.24 tff(12324,plain,
% 2.04/2.24 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12180, 116, 11792, 11112, 10252])).
% 2.04/2.24 tff(12325,plain,
% 2.04/2.24 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[89, 21, 12324, 56])).
% 2.04/2.24 tff(12326,plain,
% 2.04/2.24 (~r(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7618, 12325, 67])).
% 2.04/2.24 tff(12327,plain,
% 2.04/2.24 (b(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1174, 12326])).
% 2.04/2.24 tff(12328,plain,
% 2.04/2.24 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12167, 116, 11792, 11112, 10252])).
% 2.04/2.24 tff(12329,plain,
% 2.04/2.24 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[105, 12328])).
% 2.04/2.24 tff(12330,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12170, 12329, 11792, 155, 67, 11809])).
% 2.04/2.24 tff(12331,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3951, 12330])).
% 2.04/2.24 tff(12332,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4984, 77, 12329, 12331])).
% 2.04/2.24 tff(12333,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[226, 12332])).
% 2.04/2.24 tff(12334,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12191, 116, 12333, 7113, 12327, 12323])).
% 2.04/2.24 tff(12335,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12336,plain,
% 2.04/2.24 (~r(s(s(s(z))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12335, 155])).
% 2.04/2.24 tff(12337,plain,
% 2.04/2.24 (b(s(s(s(z))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[63, 12336])).
% 2.04/2.24 tff(12338,plain,
% 2.04/2.24 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11132, 2442, 12337])).
% 2.04/2.24 tff(12339,plain,
% 2.04/2.24 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[105, 12338])).
% 2.04/2.24 tff(12340,plain,
% 2.04/2.24 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2791, 116, 12337, 7113, 2442])).
% 2.04/2.24 tff(12341,plain,
% 2.04/2.24 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[89, 21, 12340, 56])).
% 2.04/2.24 tff(12342,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5905, 3987, 12341])).
% 2.04/2.24 tff(12343,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[226, 12342])).
% 2.04/2.24 tff(12344,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12191, 116, 12343, 7113, 2442])).
% 2.04/2.24 tff(12345,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[247, 12344])).
% 2.04/2.24 tff(12346,plain,
% 2.04/2.24 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8864, 12345, 155])).
% 2.04/2.24 tff(12347,plain,
% 2.04/2.24 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[325, 12346])).
% 2.04/2.24 tff(12348,plain,
% 2.04/2.24 (~b(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11126, 12347, 12339, 3987])).
% 2.04/2.24 tff(12349,plain,
% 2.04/2.24 (~(s(s(z)) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2038, 12348, 12321])).
% 2.04/2.24 tff(12350,plain,
% 2.04/2.24 (r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[426, 12349, 1])).
% 2.04/2.24 tff(12351,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11856, 12343, 2442, 1055])).
% 2.04/2.24 tff(12352,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[247, 12351])).
% 2.04/2.24 tff(12353,plain,
% 2.04/2.24 (~r(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5025, 2235, 428])).
% 2.04/2.24 tff(12354,plain,
% 2.04/2.24 (~r(s(s(s(z))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3961, 228, 3987])).
% 2.04/2.24 tff(12355,plain,
% 2.04/2.24 (b(s(s(s(z))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[63, 12354])).
% 2.04/2.24 tff(12356,plain,
% 2.04/2.24 (~r(s(s(s(z))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4976, 2235, 428])).
% 2.04/2.24 tff(12357,plain,
% 2.04/2.24 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4113, 4094, 3986])).
% 2.04/2.24 tff(12358,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2650, 3470, 228])).
% 2.04/2.24 tff(12359,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1596, 12358, 12357])).
% 2.04/2.24 tff(12360,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2407, 1455, 12355])).
% 2.04/2.24 tff(12361,plain,
% 2.04/2.24 (b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1345, 12360, 4094])).
% 2.04/2.24 tff(12362,plain,
% 2.04/2.24 (~b(s(s(s(z))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2767, 12361, 1055, 12355])).
% 2.04/2.24 tff(12363,plain,
% 2.04/2.24 (s(s(s(z))) = elem!1),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2725, 12362, 2719])).
% 2.04/2.24 tff(12364,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5534, 12363, 12359, 3986])).
% 2.04/2.24 tff(12365,plain,(b(elem!1, z) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | r(elem!1, s(s(s(z)))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12366,plain,
% 2.04/2.24 (b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12365, 12356, 3986, 1055, 228, 12353, 439])).
% 2.04/2.24 tff(12367,plain,
% 2.04/2.24 (~b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5469, 12366, 1055, 12355])).
% 2.04/2.24 tff(12368,plain,
% 2.04/2.24 (elem!1 = s(s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1345, 12367, 12353])).
% 2.04/2.24 tff(12369,plain,
% 2.04/2.24 (s(elem!1) = s(s(s(s(z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12368])).
% 2.04/2.24 tff(12370,plain,
% 2.04/2.24 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12369])).
% 2.04/2.24 tff(12371,plain,
% 2.04/2.24 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.04/2.24 inference(symmetry,[status(thm)],[12370])).
% 2.04/2.24 tff(12372,plain,
% 2.04/2.24 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12371])).
% 2.04/2.24 tff(12373,plain,
% 2.04/2.24 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[12372])).
% 2.04/2.24 tff(12374,plain,
% 2.04/2.24 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12370])).
% 2.04/2.24 tff(12375,plain,
% 2.04/2.24 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.04/2.24 inference(symmetry,[status(thm)],[12374])).
% 2.04/2.24 tff(12376,plain,
% 2.04/2.24 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5016, 2235, 3987])).
% 2.04/2.24 tff(12377,plain,
% 2.04/2.24 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6477, 116, 1055, 12355, 175, 12376])).
% 2.04/2.24 tff(12378,plain,
% 2.04/2.24 ((s(s(s(s(s(z))))) = s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5816, 21, 12377])).
% 2.04/2.24 tff(12379,plain,
% 2.04/2.24 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12378, 5783])).
% 2.04/2.24 tff(12380,plain,
% 2.04/2.24 (r(s(s(elem!1)), s(z))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12379, 12375])).
% 2.04/2.24 tff(12381,plain,
% 2.04/2.24 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12368])).
% 2.04/2.24 tff(12382,plain,
% 2.04/2.24 (b(z, s(s(s(z))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[1055, 12381])).
% 2.04/2.24 tff(12383,plain,
% 2.04/2.24 (~b(z, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5827, 116, 12355, 12382, 175])).
% 2.04/2.24 tff(12384,plain,
% 2.04/2.24 (r(z, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[289, 12383])).
% 2.04/2.24 tff(12385,plain,
% 2.04/2.24 (~r(z, s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3185, 12384, 12380])).
% 2.04/2.24 tff(12386,plain,
% 2.04/2.24 (b(z, s(s(elem!1)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[514, 12385])).
% 2.04/2.24 tff(12387,plain,
% 2.04/2.24 (b(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12386, 12373])).
% 2.04/2.24 tff(12388,plain,
% 2.04/2.24 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5238, 116, 12355, 12382, 12376])).
% 2.04/2.24 tff(12389,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12388, 12387])).
% 2.04/2.24 tff(12390,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | b(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = z) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12391,plain,
% 2.04/2.24 (~r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12390, 12352, 11792, 3986, 12339, 7118, 1055])).
% 2.04/2.24 tff(12392,plain,
% 2.04/2.24 (s(s(z)) = elem!1),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[426, 12391, 1])).
% 2.04/2.24 tff(12393,plain,
% 2.04/2.24 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8864, 12352, 155])).
% 2.04/2.24 tff(12394,plain,
% 2.04/2.24 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[325, 12393])).
% 2.04/2.24 tff(12395,plain,
% 2.04/2.24 (~b(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11126, 12394, 12339, 3987])).
% 2.04/2.24 tff(12396,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2038, 12395, 12392, 12321])).
% 2.04/2.24 tff(12397,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(z)), elem!1) | (~b(z, elem!1)) | (~r(s(z), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12398,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12397, 1055, 1, 155, 2442])).
% 2.04/2.24 tff(12399,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12400,plain,
% 2.04/2.24 (((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12401,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12400])).
% 2.04/2.24 tff(12402,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[12401, 12399])).
% 2.04/2.24 tff(12403,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(12404,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12403, 12402])).
% 2.04/2.24 tff(12405,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12404, 116, 1055, 12337, 12398, 11792])).
% 2.04/2.24 tff(12406,plain,
% 2.04/2.24 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2054, 21, 12405])).
% 2.04/2.24 tff(12407,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12406, 2044])).
% 2.04/2.24 tff(12408,plain,
% 2.04/2.24 (~r(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8860, 77, 11809, 12407])).
% 2.04/2.24 tff(12409,plain,
% 2.04/2.24 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3941, 116, 1055, 12337, 12398, 11792])).
% 2.04/2.24 tff(12410,plain,
% 2.04/2.24 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[325, 12409])).
% 2.04/2.24 tff(12411,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8864, 12410, 155])).
% 2.04/2.24 tff(12412,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[247, 12411])).
% 2.04/2.24 tff(12413,plain,
% 2.04/2.24 (~b(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3100, 12412, 12337, 12398])).
% 2.04/2.24 tff(12414,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1576, 21, 12413, 12408, 1563])).
% 2.04/2.24 tff(12415,plain,((~b(z, elem!1)) | (~r(s(z), z)) | b(s(s(z)), elem!1) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12416,plain,
% 2.04/2.24 (~b(z, elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12415, 2442, 1, 155])).
% 2.04/2.24 tff(12417,plain,
% 2.04/2.24 (r(z, elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1044, 12416, 7119])).
% 2.04/2.24 tff(12418,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3287, 12345, 12417])).
% 2.04/2.24 tff(12419,plain,
% 2.04/2.24 (~(elem!1 = s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3669, 12321])).
% 2.04/2.24 tff(12420,plain,
% 2.04/2.24 (~r(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[791, 12417, 11809])).
% 2.04/2.24 tff(12421,plain,
% 2.04/2.24 (b(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[633, 12420, 12419])).
% 2.04/2.24 tff(12422,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11331, 12347, 12321, 12421])).
% 2.04/2.24 tff(12423,plain,
% 2.04/2.24 (s(s(s(s(z)))) = elem!1),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1596, 12422, 12418])).
% 2.04/2.24 tff(12424,plain,
% 2.04/2.24 (r(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4113, 12423, 3986])).
% 2.04/2.24 tff(12425,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[5025, 12424, 12350, 12339])).
% 2.04/2.24 tff(12426,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(z)), elem!1) | (~r(s(z), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12427,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12426, 2442, 155, 1])).
% 2.04/2.24 tff(12428,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12429,plain,
% 2.04/2.24 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(12430,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12429])).
% 2.04/2.24 tff(12431,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[12430, 12428])).
% 2.04/2.24 tff(12432,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(12433,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[12432, 12431])).
% 2.04/2.24 tff(12434,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12433, 116, 12337, 12427, 2442, 11792])).
% 2.04/2.24 tff(12435,plain,
% 2.04/2.24 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2054, 21, 12434])).
% 2.04/2.24 tff(12436,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12435, 2044])).
% 2.04/2.24 tff(12437,plain,
% 2.04/2.24 (~r(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8860, 77, 11809, 12436])).
% 2.04/2.24 tff(12438,plain,
% 2.04/2.24 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2801, 116, 12337, 12427, 2442, 11792])).
% 2.04/2.24 tff(12439,plain,
% 2.04/2.24 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[325, 12438])).
% 2.04/2.24 tff(12440,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8864, 12439, 155])).
% 2.04/2.24 tff(12441,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[247, 12440])).
% 2.04/2.24 tff(12442,plain,
% 2.04/2.24 (~b(z, s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3100, 12441, 12337, 12427])).
% 2.04/2.24 tff(12443,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1576, 21, 12442, 12437, 1563])).
% 2.04/2.24 tff(12444,plain,((~b(z, s(s(z)))) | (~r(s(z), z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(12445,plain,
% 2.04/2.24 (~b(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[12444, 155, 1])).
% 2.04/2.24 tff(12446,plain,
% 2.04/2.24 (r(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1174, 12445])).
% 2.04/2.24 tff(12447,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11167, 12446, 155])).
% 2.04/2.24 tff(12448,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[247, 12447])).
% 2.04/2.24 tff(12449,plain,
% 2.04/2.24 (r(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1174, 6516])).
% 2.04/2.24 tff(12450,plain,
% 2.04/2.24 (~r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[10758, 448, 1212])).
% 2.04/2.24 tff(12451,plain,
% 2.04/2.24 (s(s(z)) = elem!1),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[426, 12450, 1])).
% 2.04/2.24 tff(12452,plain,
% 2.04/2.24 (s(s(s(z))) = s(elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12451])).
% 2.04/2.24 tff(12453,plain,
% 2.04/2.24 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12452])).
% 2.04/2.24 tff(12454,plain,
% 2.04/2.24 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[12453])).
% 2.04/2.24 tff(12455,plain,
% 2.04/2.24 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12454])).
% 2.04/2.24 tff(12456,plain,
% 2.04/2.24 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(elem!1)))),
% 2.04/2.24 inference(symmetry,[status(thm)],[12455])).
% 2.04/2.24 tff(12457,plain,
% 2.04/2.24 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[529, 12451, 7119])).
% 2.04/2.24 tff(12458,plain,
% 2.04/2.24 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[836, 12451, 12457])).
% 2.04/2.24 tff(12459,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8306, 12458])).
% 2.04/2.24 tff(12460,plain,
% 2.04/2.24 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12451])).
% 2.04/2.24 tff(12461,plain,
% 2.04/2.24 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.04/2.24 inference(transitivity,[status(thm)],[12460, 591])).
% 2.04/2.24 tff(12462,plain,
% 2.04/2.24 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[12461, 1743])).
% 2.04/2.24 tff(12463,plain,
% 2.04/2.24 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12462])).
% 2.04/2.24 tff(12464,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(z))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[100, 12463])).
% 2.04/2.24 tff(12465,plain,
% 2.04/2.24 (s(elem!1) = s(s(s(z)))),
% 2.04/2.24 inference(symmetry,[status(thm)],[12452])).
% 2.04/2.24 tff(12466,plain,
% 2.04/2.24 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12465])).
% 2.04/2.24 tff(12467,plain,
% 2.04/2.24 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12466])).
% 2.04/2.24 tff(12468,plain,
% 2.04/2.24 (b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11282, 12451])).
% 2.04/2.24 tff(12469,plain,
% 2.04/2.24 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12452])).
% 2.04/2.24 tff(12470,plain,
% 2.04/2.24 (b(s(z), s(elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[11792, 12469])).
% 2.04/2.24 tff(12471,plain,
% 2.04/2.24 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[12452])).
% 2.04/2.24 tff(12472,plain,
% 2.04/2.24 (b(s(elem!1), z)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[2247, 12471])).
% 2.04/2.24 tff(12473,plain,
% 2.04/2.24 (~r(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[791, 448, 293])).
% 2.04/2.24 tff(12474,plain,
% 2.04/2.24 (b(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[633, 12473, 12419])).
% 2.04/2.24 tff(12475,plain,
% 2.04/2.24 (~b(s(s(elem!1)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[11564, 116, 616, 12321, 667])).
% 2.04/2.24 tff(12476,plain,
% 2.04/2.24 (r(s(s(elem!1)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[808, 12475])).
% 2.04/2.24 tff(12477,plain,
% 2.04/2.24 (~r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3185, 12476, 293])).
% 2.04/2.25 tff(12478,plain,
% 2.04/2.25 (b(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[514, 12477])).
% 2.04/2.25 tff(12479,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12480,plain,
% 2.04/2.25 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12481,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12480])).
% 2.04/2.25 tff(12482,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[12481, 12479])).
% 2.04/2.25 tff(12483,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(12484,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12483, 12482])).
% 2.04/2.25 tff(12485,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12484, 116, 537, 616, 12478, 2844, 4041])).
% 2.04/2.25 tff(12486,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12487,plain,
% 2.04/2.25 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12486, 4041, 2844, 537, 293, 12474])).
% 2.04/2.25 tff(12488,plain,
% 2.04/2.25 (r(s(s(elem!1)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[743, 12487, 574])).
% 2.04/2.25 tff(12489,plain,
% 2.04/2.25 (~r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3440, 12488, 448])).
% 2.04/2.25 tff(12490,plain,
% 2.04/2.25 (b(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[514, 12489])).
% 2.04/2.25 tff(12491,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6761, 116, 12321, 12490, 2844, 4041, 4055])).
% 2.04/2.25 tff(12492,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(elem!1, z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12493,plain,
% 2.04/2.25 (~b(elem!1, s(elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12492, 12472, 12470, 448, 12457, 12468, 293])).
% 2.04/2.25 tff(12494,plain,
% 2.04/2.25 (~b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12493, 12467])).
% 2.04/2.25 tff(12495,plain,
% 2.04/2.25 (r(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1345, 12494, 12464])).
% 2.04/2.25 tff(12496,plain,
% 2.04/2.25 (~r(elem!1, s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12018, 12495, 3953])).
% 2.04/2.25 tff(12497,plain,
% 2.04/2.25 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1068, 12496, 12459])).
% 2.04/2.25 tff(12498,plain,
% 2.04/2.25 (b(elem!1, s(s(elem!1)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12497, 12456])).
% 2.04/2.25 tff(12499,plain,
% 2.04/2.25 (~(s(z) = elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1984, 12419])).
% 2.04/2.25 tff(12500,plain,
% 2.04/2.25 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12465])).
% 2.04/2.25 tff(12501,plain,
% 2.04/2.25 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.04/2.25 inference(symmetry,[status(thm)],[12500])).
% 2.04/2.25 tff(12502,plain,
% 2.04/2.25 (r(elem!1, s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12495, 12501])).
% 2.04/2.25 tff(12503,plain,
% 2.04/2.25 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12453, 12452])).
% 2.04/2.25 tff(12504,plain,
% 2.04/2.25 (r(s(s(elem!1)), s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[3953, 12503])).
% 2.04/2.25 tff(12505,plain,
% 2.04/2.25 (~r(s(s(elem!1)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11877, 77, 12504, 12502])).
% 2.04/2.25 tff(12506,plain,
% 2.04/2.25 (b(s(s(elem!1)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[743, 12505, 12457])).
% 2.04/2.25 tff(12507,plain,
% 2.04/2.25 (~r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3702, 12506, 12499, 448, 293, 12498])).
% 2.04/2.25 tff(12508,plain,
% 2.04/2.25 (b(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[514, 12507])).
% 2.04/2.25 tff(12509,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12510,plain,
% 2.04/2.25 (((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12511,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12510])).
% 2.04/2.25 tff(12512,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[12511, 12509])).
% 2.04/2.25 tff(12513,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(12514,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12513, 12512])).
% 2.04/2.25 tff(12515,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12514, 116, 12468, 12506, 12508, 12498])).
% 2.04/2.25 tff(12516,plain,((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(s(s(z)), elem!1) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12517,plain,
% 2.04/2.25 (~r(z, elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12516, 3953, 293, 2247, 1, 12449])).
% 2.04/2.25 tff(12518,plain,
% 2.04/2.25 (b(z, elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1044, 12517, 7119])).
% 2.04/2.25 tff(12519,plain,
% 2.04/2.25 (~r(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9352, 2235, 12449])).
% 2.04/2.25 tff(12520,plain,
% 2.04/2.25 (b(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11399, 12519])).
% 2.04/2.25 tff(12521,plain,
% 2.04/2.25 (~(s(s(z)) = elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6518, 1055, 6516])).
% 2.04/2.25 tff(12522,plain,
% 2.04/2.25 (r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[426, 12521, 1])).
% 2.04/2.25 tff(12523,plain,
% 2.04/2.25 (~r(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5025, 12522, 2235])).
% 2.04/2.25 tff(12524,plain,
% 2.04/2.25 (b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1345, 12523, 1620])).
% 2.04/2.25 tff(12525,plain,
% 2.04/2.25 (~r(s(s(s(z))), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4976, 12522, 2235])).
% 2.04/2.25 tff(12526,plain,
% 2.04/2.25 (b(s(s(s(z))), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2725, 12525, 11310])).
% 2.04/2.25 tff(12527,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12528,plain,
% 2.04/2.25 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12529,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12528])).
% 2.04/2.25 tff(12530,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[12529, 12527])).
% 2.04/2.25 tff(12531,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(12532,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12531, 12530])).
% 2.04/2.25 tff(12533,plain,
% 2.04/2.25 ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12532, 116])).
% 2.04/2.25 tff(12534,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12533, 12526, 12524, 12520, 1055])).
% 2.04/2.25 tff(12535,plain,((~b(z, elem!1)) | (elem!1 = s(s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(z)), elem!1) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12536,plain,
% 2.04/2.25 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12535, 3467, 1, 6516, 1055])).
% 2.04/2.25 tff(12537,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[105, 12536])).
% 2.04/2.25 tff(12538,plain,
% 2.04/2.25 (r(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[545, 1455, 7118])).
% 2.04/2.25 tff(12539,plain,
% 2.04/2.25 (~r(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2095, 12538, 293])).
% 2.04/2.25 tff(12540,plain,
% 2.04/2.25 (b(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[633, 12539, 12419])).
% 2.04/2.25 tff(12541,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12542,plain,
% 2.04/2.25 (((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12543,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12542])).
% 2.04/2.25 tff(12544,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[12543, 12541])).
% 2.04/2.25 tff(12545,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(12546,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12545, 12544])).
% 2.04/2.25 tff(12547,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12546, 116, 1055, 12540, 2247, 7113, 12537])).
% 2.04/2.25 tff(12548,plain,(b(elem!1, z) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | b(s(s(z)), elem!1) | b(z, s(s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12549,plain,
% 2.04/2.25 (b(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12548, 12518, 2247, 1, 6516, 293])).
% 2.04/2.25 tff(12550,plain,
% 2.04/2.25 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8501, 116, 12518, 12549, 2247, 7113])).
% 2.04/2.25 tff(12551,plain,
% 2.04/2.25 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[105, 12550])).
% 2.04/2.25 tff(12552,plain,
% 2.04/2.25 (elem!1 = s(s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12535, 12551, 1, 6516, 12518])).
% 2.04/2.25 tff(12553,plain,
% 2.04/2.25 (s(elem!1) = s(s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12552])).
% 2.04/2.25 tff(12554,plain,
% 2.04/2.25 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12553])).
% 2.04/2.25 tff(12555,plain,
% 2.04/2.25 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12554])).
% 2.04/2.25 tff(12556,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.04/2.25 inference(symmetry,[status(thm)],[12555])).
% 2.04/2.25 tff(12557,plain,
% 2.04/2.25 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12556])).
% 2.04/2.25 tff(12558,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5016, 12551, 3953])).
% 2.04/2.25 tff(12559,plain,
% 2.04/2.25 (~r(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9352, 12551, 12449])).
% 2.04/2.25 tff(12560,plain,
% 2.04/2.25 (b(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11399, 12559])).
% 2.04/2.25 tff(12561,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12562,plain,
% 2.04/2.25 (((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12563,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12562])).
% 2.04/2.25 tff(12564,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[12563, 12561])).
% 2.04/2.25 tff(12565,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(12566,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12565, 12564])).
% 2.04/2.25 tff(12567,plain,
% 2.04/2.25 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12566, 116, 2247, 12560, 11792, 12558])).
% 2.04/2.25 tff(12568,plain,
% 2.04/2.25 (~b(s(s(elem!1)), s(z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12567, 12557])).
% 2.04/2.25 tff(12569,plain,
% 2.04/2.25 (r(s(s(elem!1)), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[808, 12568])).
% 2.04/2.25 tff(12570,plain,
% 2.04/2.25 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.04/2.25 inference(symmetry,[status(thm)],[12554])).
% 2.04/2.25 tff(12571,plain,
% 2.04/2.25 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(elem!1)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12570])).
% 2.04/2.25 tff(12572,plain,
% 2.04/2.25 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(z, s(s(elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12571])).
% 2.04/2.25 tff(12573,plain,
% 2.04/2.25 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5238, 116, 2247, 12560, 12558])).
% 2.04/2.25 tff(12574,plain,
% 2.04/2.25 (~b(z, s(s(elem!1)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12573, 12572])).
% 2.04/2.25 tff(12575,plain,
% 2.04/2.25 (r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[514, 12574])).
% 2.04/2.25 tff(12576,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3185, 12575, 12569, 293])).
% 2.04/2.25 tff(12577,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | b(s(s(z)), elem!1) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12578,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12577, 11809, 12337, 1, 12445])).
% 2.04/2.25 tff(12579,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3951, 12578])).
% 2.04/2.25 tff(12580,plain,
% 2.04/2.25 (~b(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2255, 12579, 12337, 12448])).
% 2.04/2.25 tff(12581,plain,
% 2.04/2.25 (r(z, s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11399, 12580])).
% 2.04/2.25 tff(12582,plain,
% 2.04/2.25 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[9352, 12581, 12446])).
% 2.04/2.25 tff(12583,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[105, 12582])).
% 2.04/2.25 tff(12584,plain,
% 2.04/2.25 (b(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12548, 1055, 2247, 1, 6516, 293])).
% 2.04/2.25 tff(12585,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8501, 116, 1055, 12584, 2247, 7113, 27])).
% 2.04/2.25 tff(12586,plain,((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | b(s(s(z)), elem!1) | b(z, s(s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12587,plain,
% 2.04/2.25 (~b(z, elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12586, 12337, 12583, 1, 12445, 11809])).
% 2.04/2.25 tff(12588,plain,
% 2.04/2.25 (r(z, elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1044, 12587, 7119])).
% 2.04/2.25 tff(12589,plain,
% 2.04/2.25 (~r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[10758, 12588, 12446])).
% 2.04/2.25 tff(12590,plain,
% 2.04/2.25 (s(s(z)) = elem!1),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[426, 12589, 1])).
% 2.04/2.25 tff(12591,plain,
% 2.04/2.25 (b(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11282, 12590])).
% 2.04/2.25 tff(12592,plain,
% 2.04/2.25 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[529, 12590, 7119])).
% 2.04/2.25 tff(12593,plain,
% 2.04/2.25 (s(s(s(z))) = s(elem!1)),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12590])).
% 2.04/2.25 tff(12594,plain,
% 2.04/2.25 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12593])).
% 2.04/2.25 tff(12595,plain,
% 2.04/2.25 (b(s(z), s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[11792, 12594])).
% 2.04/2.25 tff(12596,plain,
% 2.04/2.25 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12593])).
% 2.04/2.25 tff(12597,plain,
% 2.04/2.25 (b(s(elem!1), z)),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12337, 12596])).
% 2.04/2.25 tff(12598,plain,
% 2.04/2.25 (s(elem!1) = s(s(s(z)))),
% 2.04/2.25 inference(symmetry,[status(thm)],[12593])).
% 2.04/2.25 tff(12599,plain,
% 2.04/2.25 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12598])).
% 2.04/2.25 tff(12600,plain,
% 2.04/2.25 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.04/2.25 inference(symmetry,[status(thm)],[12599])).
% 2.04/2.25 tff(12601,plain,
% 2.04/2.25 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12590])).
% 2.04/2.25 tff(12602,plain,
% 2.04/2.25 (b(elem!1, s(s(s(z))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12583, 12601])).
% 2.04/2.25 tff(12603,plain,
% 2.04/2.25 (b(elem!1, s(elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12602, 12600])).
% 2.04/2.25 tff(12604,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12492, 12603, 12597, 12595, 12588, 12592, 12591, 11809])).
% 2.04/2.25 tff(12605,plain,((~r(s(z), z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12606,plain,
% 2.04/2.25 (~r(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12605, 1])).
% 2.04/2.25 tff(12607,plain,
% 2.04/2.25 (b(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[210, 12606])).
% 2.04/2.25 tff(12608,plain,
% 2.04/2.25 (~b(z, s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12213, 12607])).
% 2.04/2.25 tff(12609,plain,
% 2.04/2.25 (r(z, s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1174, 12608])).
% 2.04/2.25 tff(12610,plain,
% 2.04/2.25 (~b(z, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12201, 12607])).
% 2.04/2.25 tff(12611,plain,
% 2.04/2.25 (r(z, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[289, 12610])).
% 2.04/2.25 tff(12612,plain,
% 2.04/2.25 (r(z, elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6099, 12611, 12321, 7119, 12607])).
% 2.04/2.25 tff(12613,plain,
% 2.04/2.25 (~r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[10758, 12612, 12609])).
% 2.04/2.25 tff(12614,plain,
% 2.04/2.25 (s(s(z)) = elem!1),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[426, 12613, 1])).
% 2.04/2.25 tff(12615,plain,
% 2.04/2.25 (~(s(s(elem!1)) = elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[529, 12614, 7119])).
% 2.04/2.25 tff(12616,plain,
% 2.04/2.25 (~r(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[791, 12612, 12611])).
% 2.04/2.25 tff(12617,plain,
% 2.04/2.25 (b(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[633, 12616, 12419])).
% 2.04/2.25 tff(12618,plain,
% 2.04/2.25 (b(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11282, 12614])).
% 2.04/2.25 tff(12619,plain,
% 2.04/2.25 (~b(z, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12201, 270])).
% 2.04/2.25 tff(12620,plain,
% 2.04/2.25 (r(z, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[289, 12619])).
% 2.04/2.25 tff(12621,plain,
% 2.04/2.25 (~r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3185, 12476, 12620])).
% 2.04/2.25 tff(12622,plain,
% 2.04/2.25 (b(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[514, 12621])).
% 2.04/2.25 tff(12623,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12624,plain,
% 2.04/2.25 (((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(12625,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[12624])).
% 2.04/2.25 tff(12626,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[12625, 12623])).
% 2.04/2.25 tff(12627,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(12628,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[12627, 12626])).
% 2.04/2.25 tff(12629,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12628, 116, 537, 616, 12321, 270, 12622])).
% 2.04/2.25 tff(12630,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12631,plain,
% 2.04/2.25 (~b(s(s(elem!1)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12630, 12618, 12607, 12617])).
% 2.04/2.25 tff(12632,plain,
% 2.04/2.25 (r(s(s(elem!1)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[743, 12631, 12615])).
% 2.04/2.25 tff(12633,plain,
% 2.04/2.25 (~r(s(s(elem!1)), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1422, 77, 12612, 12632])).
% 2.04/2.25 tff(12634,plain,
% 2.04/2.25 (b(s(s(elem!1)), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3219, 12633])).
% 2.04/2.25 tff(12635,plain,
% 2.04/2.25 (~r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3440, 12632, 12612])).
% 2.04/2.25 tff(12636,plain,
% 2.04/2.25 (b(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[514, 12635])).
% 2.04/2.25 tff(12637,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11591, 116, 12618, 12321, 12607, 12636, 12634])).
% 2.04/2.25 tff(12638,plain,(b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(12639,plain,
% 2.04/2.25 (~b(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11463, 12638, 12321])).
% 2.04/2.25 tff(12640,plain,
% 2.04/2.25 (r(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[633, 12639, 12419])).
% 2.04/2.25 tff(12641,plain,
% 2.04/2.25 (~r(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[11807, 271])).
% 2.04/2.25 tff(12642,plain,
% 2.04/2.25 (~b(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[12201, 271])).
% 2.04/2.25 tff(12643,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[210, 12642, 12641])).
% 2.04/2.26 tff(12644,plain,(~b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12645,plain,
% 2.04/2.26 (r(z, s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[289, 12644])).
% 2.04/2.26 tff(12646,plain,
% 2.04/2.26 (~r(elem!1, z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2095, 12645, 12640])).
% 2.04/2.26 tff(12647,plain,
% 2.04/2.26 (b(elem!1, z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[545, 439, 12646])).
% 2.04/2.26 tff(12648,plain,
% 2.04/2.26 (~r(z, elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[791, 12645, 12640])).
% 2.04/2.26 tff(12649,plain,
% 2.04/2.26 (b(z, elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1044, 446, 12648])).
% 2.04/2.26 tff(12650,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8043, 12649, 12647, 12638])).
% 2.04/2.26 tff(12651,plain,(elem!1 = z), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12652,plain,
% 2.04/2.26 (~(s(s(s(z))) = elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1749, 2573])).
% 2.04/2.26 tff(12653,plain,
% 2.04/2.26 (s(s(s(z))) = elem!1),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[1366, 591])).
% 2.04/2.26 tff(12654,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2688, 12653])).
% 2.04/2.26 tff(12655,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12656,plain,
% 2.04/2.26 (~(elem!1 = s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12655, 12652])).
% 2.04/2.26 tff(12657,plain,
% 2.04/2.26 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2411])).
% 2.04/2.26 tff(12658,plain,
% 2.04/2.26 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[12657])).
% 2.04/2.26 tff(12659,plain,
% 2.04/2.26 (b(s(elem!1), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[11792, 12658])).
% 2.04/2.26 tff(12660,plain,
% 2.04/2.26 (b(s(elem!1), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6119, 2573, 12321])).
% 2.04/2.26 tff(12661,plain,
% 2.04/2.26 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[404])).
% 2.04/2.26 tff(12662,plain,
% 2.04/2.26 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.26 inference(symmetry,[status(thm)],[12661])).
% 2.04/2.26 tff(12663,plain,
% 2.04/2.26 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[404])).
% 2.04/2.26 tff(12664,plain,
% 2.04/2.26 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.04/2.26 inference(transitivity,[status(thm)],[12663, 2897])).
% 2.04/2.26 tff(12665,plain,
% 2.04/2.26 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[12664])).
% 2.04/2.26 tff(12666,plain,
% 2.04/2.26 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12665])).
% 2.04/2.26 tff(12667,plain,
% 2.04/2.26 (~(elem!1 = s(s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[242, 12666])).
% 2.04/2.26 tff(12668,plain,
% 2.04/2.26 (b(s(z), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6442, 404, 12321])).
% 2.04/2.26 tff(12669,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[11620, 67, 12321, 2573])).
% 2.04/2.26 tff(12670,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1340, 27, 176, 12638])).
% 2.04/2.26 tff(12671,plain,
% 2.04/2.26 (r(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1345, 12670, 12656])).
% 2.04/2.26 tff(12672,plain,
% 2.04/2.26 (r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2488, 12671, 404])).
% 2.04/2.26 tff(12673,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6403, 27, 11792, 176])).
% 2.04/2.26 tff(12674,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1380, 12673])).
% 2.04/2.26 tff(12675,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12676,plain,
% 2.04/2.26 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12677,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12676])).
% 2.04/2.26 tff(12678,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[12677, 12675])).
% 2.04/2.26 tff(12679,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(12680,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12679, 12678])).
% 2.04/2.26 tff(12681,plain,
% 2.04/2.26 (~r(z, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12680, 77, 12674, 12672])).
% 2.04/2.26 tff(12682,plain,
% 2.04/2.26 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3778, 21, 12681])).
% 2.04/2.26 tff(12683,plain,
% 2.04/2.26 (b(z, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12682, 3768])).
% 2.04/2.26 tff(12684,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = z)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[404])).
% 2.04/2.26 tff(12685,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.26 inference(symmetry,[status(thm)],[12684])).
% 2.04/2.26 tff(12686,plain,
% 2.04/2.26 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12685])).
% 2.04/2.26 tff(12687,plain,
% 2.04/2.26 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[895, 12686])).
% 2.04/2.26 tff(12688,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2434])).
% 2.04/2.26 tff(12689,plain,
% 2.04/2.26 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12688])).
% 2.04/2.26 tff(12690,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8940, 77, 12645, 12674, 12672])).
% 2.04/2.26 tff(12691,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12690, 12689])).
% 2.04/2.26 tff(12692,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[885, 12691, 12687])).
% 2.04/2.26 tff(12693,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4869, 12692, 404])).
% 2.04/2.26 tff(12694,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12695,plain,
% 2.04/2.26 (((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12696,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12695])).
% 2.04/2.26 tff(12697,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[12696, 12694])).
% 2.04/2.26 tff(12698,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(12699,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12698, 12697])).
% 2.04/2.26 tff(12700,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12699, 116, 12668, 7113, 11112, 12693, 12683])).
% 2.04/2.26 tff(12701,plain,((~b(s(s(z)), s(s(s(z))))) | (~(elem!1 = z)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12702,plain,
% 2.04/2.26 (~b(s(s(z)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12701, 12669, 404])).
% 2.04/2.26 tff(12703,plain,
% 2.04/2.26 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[105, 12702])).
% 2.04/2.26 tff(12704,plain,
% 2.04/2.26 (~r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[9352, 12703, 1212])).
% 2.04/2.26 tff(12705,plain,
% 2.04/2.26 (b(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[11399, 12704])).
% 2.04/2.26 tff(12706,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2549, 228, 1212])).
% 2.04/2.26 tff(12707,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[226, 12706])).
% 2.04/2.26 tff(12708,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12709,plain,
% 2.04/2.26 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12710,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12709])).
% 2.04/2.26 tff(12711,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[12710, 12708])).
% 2.04/2.26 tff(12712,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(12713,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12712, 12711])).
% 2.04/2.26 tff(12714,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12713, 116, 270, 12707, 255, 10695, 11792])).
% 2.04/2.26 tff(12715,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12716,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12715, 12705, 12668, 67, 1212])).
% 2.04/2.26 tff(12717,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[247, 12716])).
% 2.04/2.26 tff(12718,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12719,plain,
% 2.04/2.26 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12720,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12719])).
% 2.04/2.26 tff(12721,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[12720, 12718])).
% 2.04/2.26 tff(12722,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(12723,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12722, 12721])).
% 2.04/2.26 tff(12724,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12723, 116, 270, 7113, 254, 11112, 1176])).
% 2.04/2.26 tff(12725,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12726,plain,
% 2.04/2.26 (~b(z, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12725, 12717, 12668])).
% 2.04/2.26 tff(12727,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3626, 12726, 2573])).
% 2.04/2.26 tff(12728,plain,
% 2.04/2.26 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1068, 12727, 12667])).
% 2.04/2.26 tff(12729,plain,
% 2.04/2.26 (r(z, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2440, 12728, 404])).
% 2.04/2.26 tff(12730,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12731,plain,
% 2.04/2.26 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12732,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12731])).
% 2.04/2.26 tff(12733,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[12732, 12730])).
% 2.04/2.26 tff(12734,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(12735,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12734, 12733])).
% 2.04/2.26 tff(12736,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12735, 77, 12645, 67, 2453, 1564])).
% 2.04/2.26 tff(12737,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12738,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12737, 67, 12729])).
% 2.04/2.26 tff(12739,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1146, 12738])).
% 2.04/2.26 tff(12740,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1572, 12729, 1212])).
% 2.04/2.26 tff(12741,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[226, 12740])).
% 2.04/2.26 tff(12742,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12713, 116, 12668, 12741, 12705, 12739, 11792])).
% 2.04/2.26 tff(12743,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(12744,plain,
% 2.04/2.26 (~r(s(s(s(z))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12743, 404, 1212])).
% 2.04/2.26 tff(12745,plain,
% 2.04/2.26 (b(s(s(s(z))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[63, 12744])).
% 2.04/2.26 tff(12746,plain,
% 2.04/2.26 (b(s(s(s(z))), elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12745, 12662])).
% 2.04/2.26 tff(12747,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6850, 12746, 12660, 12659])).
% 2.04/2.26 tff(12748,plain,
% 2.04/2.26 (r(elem!1, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1345, 12747, 12656])).
% 2.04/2.26 tff(12749,plain,
% 2.04/2.26 (r(z, s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2488, 12748, 404])).
% 2.04/2.26 tff(12750,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2578])).
% 2.04/2.26 tff(12751,plain,
% 2.04/2.26 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[12750])).
% 2.04/2.26 tff(12752,plain,
% 2.04/2.26 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[9352, 12749, 1212])).
% 2.04/2.26 tff(12753,plain,
% 2.04/2.26 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[105, 12752])).
% 2.04/2.26 tff(12754,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[12753, 12751])).
% 2.04/2.26 tff(12755,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6868, 12745, 12321, 12648, 11792, 12668])).
% 2.04/2.26 tff(12756,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3951, 12755])).
% 2.04/2.26 tff(12757,plain,
% 2.04/2.26 (~b(z, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[12725, 254, 12668])).
% 2.04/2.26 tff(12758,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3626, 12757, 2573])).
% 2.04/2.26 tff(12759,plain,
% 2.04/2.26 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1068, 12758, 12667])).
% 2.04/2.26 tff(12760,plain,
% 2.04/2.26 (r(z, s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2440, 12759, 404])).
% 2.04/2.26 tff(12761,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2461, 12760, 12749])).
% 2.04/2.26 tff(12762,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1146, 12761])).
% 2.04/2.26 tff(12763,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1572, 12760, 1212])).
% 2.04/2.26 tff(12764,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[226, 12763])).
% 2.04/2.26 tff(12765,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12766,plain,
% 2.04/2.26 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(12767,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[12766])).
% 2.04/2.26 tff(12768,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[12767, 12765])).
% 2.04/2.27 tff(12769,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(12770,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[12769, 12768])).
% 2.04/2.27 tff(12771,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[12770, 116, 12764, 12753, 12756, 254, 12762])).
% 2.04/2.27 tff(12772,plain,((~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(12773,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[12772, 404, 1212])).
% 2.04/2.27 tff(12774,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[247, 12773])).
% 2.04/2.27 tff(12775,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2549, 12774, 1212])).
% 2.04/2.27 tff(12776,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[226, 12775])).
% 2.04/2.27 tff(12777,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3559, 12776, 404])).
% 2.04/2.27 tff(12778,plain,
% 2.04/2.27 (~b(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3570, 12777, 12756, 12754, 12746])).
% 2.04/2.27 tff(12779,plain,
% 2.04/2.27 (r(elem!1, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1068, 12778, 12667])).
% 2.04/2.27 tff(12780,plain,
% 2.04/2.27 (r(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2440, 12779, 404])).
% 2.04/2.27 tff(12781,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2461, 12780, 12749])).
% 2.04/2.27 tff(12782,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1146, 12781])).
% 2.04/2.27 tff(12783,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(12784,plain,
% 2.04/2.27 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(12785,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[12784])).
% 2.04/2.27 tff(12786,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[12785, 12783])).
% 2.04/2.27 tff(12787,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(12788,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[12787, 12786])).
% 2.04/2.27 tff(12789,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[12788, 116, 12776, 12753, 12756, 12782])).
% 2.04/2.27 tff(12790,plain,((~(elem!1 = z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(12791,plain,
% 2.04/2.27 (~r(z, s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[12790, 12651])).
% 2.04/2.27 tff(12792,plain,
% 2.04/2.27 (b(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6442, 12651, 12321])).
% 2.04/2.27 tff(12793,plain,
% 2.04/2.27 (~b(z, s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[12213, 12792])).
% 2.04/2.27 tff(12794,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1174, 12793, 12791])).
% 2.04/2.27 % SZS output end Proof
% 2.04/2.27 % E exiting
%------------------------------------------------------------------------------